VITA
Darryl J. McCullough
Born: December 20, 1951 in Columbus, Ohio
Education:  B. A.  Ohio State University, 1972 
M. A.  University of Michigan, 1974  
Ph. D.  University of Michigan, 1978 
Graduate Advisor: Frank A. Raymond
Employment:  19721978  Graduate Teaching Assistant 
University of Michigan  
19781984  Assistant Professor of Mathematics  
University of Oklahoma  
19841988  Associate Professor of Mathematics  
University of Oklahoma  
19882007  Professor of Mathematics  
University of Oklahoma  
20072011  Presidential Professor of Mathematics  
University of Oklahoma  
2012  Professor Emeritus of Mathematics  
University of Oklahoma 
Research Interests: Lowdimensional topology and related subjects
Refereed Research Publications:
1.  Finite aspherical complexes with infinitelygenerated groups of selfhomotopyequivalences, Proc. Amer. Math. Soc. 80 (1980), 337340. 
2.  Connected sums of aspherical manifolds, Indiana Univ. Math. J. 30 (1981), 1728. 
3.  The group of homotopy equivalences for a connected sum of closed aspherical manifolds, Indiana Univ. Math. J. 30 (1981), 249260. 
4.  Homotopy groups of the space of selfhomotopyequivalences, Trans. Amer. Math. Soc. 264 (1981), 151163. 
5.  A theorem on symmetry of primitives, Arch. Math. 39 (1982), 492495. 
6.  Homotopy equivalences of punctured manifolds, Mich. Math. J. 29 (1982), 357365. 
7.^{ }  Intersections of separators and essential submanifolds of I^{N} (with Leonard R. Rubin), Fund. Math. 116 (1983), 163174. 
8.  Compact 3manifolds with infinitely generated groups of selfhomotopyequivalences, Proc. Amer. Math. Soc. 91 (1984), 625629. 
9.  Twist groups of compact 3manifolds, Topology 24 (1985), 461474. 
10.  Uniqueness of cores of noncompact 3manifolds (with Andy Miller and G. A. Swarup), J. London Math. Soc. (2) 32 (1985), 548556. 
11.  π_{1}injective mappings of compact 3manifolds (with John Kalliongis), Proc. London Math. Soc. (3) 52 (1986), 173192. 
12.  The genus 2 Torelli group is not finitely generated (with Andy Miller), Top. Appl. 22 (1986), 4349. 
13.  Homeomorphisms of 3manifolds with compressible boundary (with Andy Miller), Mem. Amer. Math. Soc. 61 (1986) no. 344, 1100. 
14.  Compact submanifolds of 3manifolds with boundary, Quarterly J. Math. Oxford (2) 37 (1986), 299307. 
15.  Automorphisms of punctured surface bundles, in Geometry and Topology: Manifolds, Varieties, and Knots, ed. C. McCrory and T. Shifrin, MarcelDekker, New York (1987), 179209. 
16.  Maps inducing isomorphisms on fundamental groups of compact 3manifolds (with John Kalliongis), J. London Math. Soc. (2) 35 (1987), 177192. 
17.  On the diffeomorphism group of a reducible 3manifold (with Harrie Hendriks), Top. Appl. 26 (1987), 2531. 
18.  Finiteness conditions for 3manifolds with boundary (with Mark Feighn), Amer. J. Math. 109 (1987), 11551169. 
19.  Virtual cohomological dimension of mapping class groups of 3manifolds (research announcement), Bull. Amer. Math. Soc. 18 (1988), 2730. 
20.^{ }  Some mdimensional compacta admitting a dense set of imbeddings into R^{2m} (with Leonard R. Rubin), Fund. Math. 133 (1989), 235243. 
21.  Manifold covers of 3orbifolds with geometric pieces (with Andy Miller), Top. Appl. 31 (1989), 169185. 
22.  Group actions on handlebodies (with Andy Miller and Bruno Zimmermann), Proc. London Math. Soc. (3) 59 (1989), 373416. 
23.  Sequentially equidistant points in metric spaces (with Leonard R. Rubin), Israel J. Math. 69 (1990), 7593. 
24.  Group actions on nonclosed 2manifolds (with Andy Miller and Bruno Zimmermann), J. Pure Appl. Algebra 64 (1990), 269292. 
25.  Finite presentation of 3manifold mapping class groups (with Allen Hatcher), Groups of SelfEquivalences and Related Topics, ed. R. Piccinini, SpringerVerlag Lecture Notes in Mathematics Vol. 1425 (1990), 4857. 
26.  Topological and algebraic automorphisms of 3manifolds, Groups of SelfEquivalences and Related Topics, ed. R. Piccinini, SpringerVerlag Lecture Notes in Mathematics Vol. 1425 (1990), 102113. 
27.  Minimal genus of abelian actions on Klein surfaces with boundary, Math. Z. 205 (1990), 421436. 
28.  Virtually geometrically finite mapping class groups of 3manifolds, J. Diff. Geom. 33 (1991), 165. 
29.  The stable genus increment for group actions on closed 2manifolds (with Andy Miller), Topology 31 (1992), 367397. 
30.  Homeotopy groups of irreducible 3manifolds which may contain twosided projective planes (with John Kalliongis), Pacific J. Math. 153 (1) (1992), 85117. 
31.  Weak concentration points for Möbius groups, Illinois J. Math. 38 (1994), 624635. 
32.  Recurrent geodesics and controlled concentration points (with Beat Aebischer and Sungbok Hong), Duke Math. J. 75 (1994), 759774. 
33.  Orientationreversing involutions of handlebodies (with John Kalliongis), Trans. Amer. Math. Soc. 348 (1996), 17391755. 
34.  Symmetric automorphisms of free products (with Andy Miller), Mem. Amer. Math. Soc. 122 (1996) no. 582, 197. 
35.  Isotopies of 3manifolds (with John Kalliongis), Top. Appl. 71 (1996), 227263. 
36.  Finiteness of classifying spaces of relative diffeomorphism groups of 3manifolds (with Allen Hatcher), Geom. Topol. 1 (1997), 91109. 
37.  Ubiquity of geometric finiteness in mapping class groups of Haken 3manifolds (with Sungbok Hong), Pacific J. Math. 188 (1999), 275301. 
38.  Concentration points for Fuchsian groups (with Sungbok Hong), Top. Appl. 105 (2000), 285303. 
39.  The topology of deformation spaces of Kleinian groups (with James W. Anderson and Richard D. Canary), Ann. of Math. 152 (2000), 693741. 
40.  Isometries of elliptic 3manifolds, J. London Math. Soc. (2) 65 (2002), 167182. 
41.  Imbeddings of free actions on handlebodies, Proc. Amer. Math. Soc. 131 (2003), 22472253. 
42.  Free actions on handlebodies (with Marcus Wanderley), J. Pure Appl. Algebra 181 (2003), 85104. 
43.  Homotopy equivalences of 3manifolds and deformation theory of Kleinian groups (with Richard D. Canary), Mem. Amer. Math. Soc. 172 (2004) no. 812, 1218. 
44.  Orientationreversing free actions on handlebodies (with Antonio Costa), J. Pure Appl. Algebra 204 (2006), 155169. 
45.  Homeomorphisms which are Dehn twists on the boundary, Alg. Geom. Topology 6 (2006), 13311340. 
46.  The tree of knot tunnels (with Sangbum Cho), Geom. Topol. 13 (2009), 769815. 
47.  Cabling sequences of tunnels of torus knots (with Sangbum Cho), Alg. Geom. Topology 9 (2009), 120. 
48.  Arc distance equals level number (with Sangbum Cho and Arim Seo), Proc. Amer. Math. Soc. 137 (2009), 28012807. 
49.  Constructing knot tunnels using giant steps (with Sangbum Cho), Proc. Amer. Math. Soc. 138 (2010), 375384. 
50.  Tunnel leveling, depth, and bridge numbers (with Sangbum Cho), Trans. Amer. Math. Soc. 353 (2011), 259280. 
51.  Writing elements of PSL(2,q) as commutators (with Marcus Wanderley), Comm. Algebra 39 (2011), 12341241. 
52.  Roots of Dehn twists (with Kashyap Rajeevsarathy), Geometriae Dedicata 151 (2011), 397409. 
53.  Diffeomorphisms of elliptic 3manifolds (with Sungbok Hong, John Kalliongis, and J. Hyam Rubinstein), Springer Verlag Lecture Notes in Mathematics 2055 (2012), 1155. 
54.  Semisimple tunnels (with Sangbum Cho), Pacific J. Math. 258 (2012), 5189. 
55.  Middle tunnels by splitting (with Sangbum Cho), Tohoku Math. J. 64 (2012), 469488. 
56.  The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold (with Teruhiko Soma), J. Diff. Geom. 93 (2013), 327353. 
57.  Iterated splitting and the classification of knot tunnels (with Sangbum Cho), J. Math. Soc. Japan 65 (2013), 116. 
58.  Nielsen equivalence of generating pairs of SL(2,q) (with Marcus Wanderley), Glasgow Math. J. 55 (2013), 481509. 
59.  The space of Heegaard splittings (with Jesse Johnson), J. Reine Angew. Math. 679 (2013), 155179. 
60.  Generating pairs and group actions, J. Pure Appl. Algebra 218 (2014), 777783. 
Refereed Research Publications (elementary topics):
61.  Recursive enumeration of Pythagorean triples (with Elizabeth Wade), College Math. J. 34 (2003), 107111. 
62.  Height and excess of Pythagorean triples, Math. Mag. 78 (2005), 2644. 
63.  Mappings of reducible 3manifolds, in Proceedings of the Semester on Topology of the Stefan Banach International Mathematical Center, ed. H. Torunczyk, Banach Center Publications, Warsaw (1986), 6176. 
64.  3Manifolds and Their Mappings, Global Analysis Research Center Lecture Notes Series Vol. 26, Seoul National University, 1995, ii + 83 pp. 
65.  Mapping class groups of 3manifolds, then and now (with Sungbok Hong), in Geometry and Topology Down Under, Contemporary Mathematics 597 (2013), 5363. 
1.  Patricia Grasse, Results on Finite Presentation of Mapping Class Groups of Certain 3Manifolds, 1986. 
2.  Sungbok Hong, MyrbergAgard Density Points and Groups of Divergence Type, 1992. 
3.  Kavita Bhatia, Pleating Coordinates For a Slice of the Deformation Space of a Hyperbolic 3Manifold With Compressible Boundary, 1997. 
4.  Arim Seo, Torus Leveling of (1,1)Knots, 2008. 
5.  Sangbum Cho, Finite Presentation of the Goeritz Group, 2008. 
6.  Kashyap Rajeevsarathy, Fractional Powers of Dehn Twists, 2011. 
External Research Funding:
1.  National Science Foundation Research Grant (198183) 
2.  National Science Foundation Research Grant (198587) 
3.  National Science Foundation Research Grant (198789) 
4.  National Science Foundation Research Grant (200103) 
5.  National Science Foundation Research Grant (200810) 
1.  Homotopy groups of the space of selfequivalences, Fourteenth Michigan Topology Conference, Michigan State University, March 18, 1978. 
2.  Homotopy groups of the space of selfhomotopyequivalences, Georgia Topology Conference, University of Georgia, July 31, 1978. 
3.  Homeomorphisms of 3manifolds with compressible boundary, Colloquium at Oklahoma State University, October 28, 1982. 
4.  Homeomorphisms of 3manifolds, Colloquium at Southwest Texas State University, December 2, 1982. 
5.  A rewriting process for some subgroups of mapping class groups, Special Session on Topological Methods in Combinatorial Group Theory, AMS Summer Meeting, Albany, New York, August 9, 1983. 
6.  The genus 2 Torelli group, Colloquium at Ruhr Universität Bochum, Bochum, West Germany, May 11, 1984. 
7.  Homotopy equivalences and homeomorphisms of compact 3manifolds, Stefan Banach International Mathematical Center, Warsaw, Poland, May 17, 1984. 
8.  Mappings of 3manifolds with compressible boundary, Colloquium at Johann Wolfgang Goethe Universität, Frankfurt, West Germany, May 25, 1984. 
9.  Twist groups of compact 3manifolds, Colloquium at Katholieke Universiteit, Nijmegen, the Netherlands, May 29, 1984. 
10.  Geometric structures on lowdimensional manifolds, Colloquium at San Jose State University, November 15, 1984. 
11.  Group actions on handlebodies, Special Session on Transformation Groups, AMS Regional Meeting, Charlotte, North Carolina, October 17, 1986. 
12.  Cohomological properties of 3manifold mapping class groups, Special Session on Geometric Methods in Group Theory, AMS Summer Meeting, Salt Lake City, Utah, August 10, 1987. 
13.  Geometric structures on lowdimensional manifolds, Colloquium at Kansas State University, October 20, 1987. 
14.  Homeomorphisms of 2manifolds and 3manifolds, Colloquium at Oklahoma State University, November 5, 1987. 
15.  Virtual cohomological dimension of 3manifold mapping class groups, Special Session on Geometric Topology, AMS Regional Meeting, Los Angeles, California, November 14, 1987. 
16.  Imbeddings of compact metric spaces, Colloquium at St. Louis University, March 7, 1988. 
17.  The stable Hurwitz problem for group actions on 2manifolds, Workshop in Geometry and Topology, University of Melbourne, Australia, June 26, 1988. 
18.  Automorphisms of groups and automorphisms of spaces, Workshop on Selfhomotopy Equivalences, Centre de Recherches Mathématiques, Montreal, Quebec, August 9, 1988. 
19.  The generalized Smale Conjecture for some nonHaken 3manifolds, Special Session on 3manifolds, AMS Regional Meeting, Lawrence, Kansas, October 28, 1988. 
20.  Group actions on nonclosed 2manifolds, Special Session on Lowdimensional Geometry, AMS Regional Meeting, Claremont, California, November 13, 1988. 
21.  A problem in metric continua, Spring Topology Conference, University of Tennessee, March 17, 1989. 
22.  Automorphisms of free products, Workshop on Arithmetic Groups, Related Groups, and Buildings, Mathematical Sciences Research Institute, Berkeley, California, May 10, 1989. 
23.  Symmetries of nonclosed surfaces, Joint Summer Research Conference on the Geometry of Riemann Surfaces and Discrete Groups, Humboldt State University, Arcata, California, July 20, 1989. 
24.  A conjectural picture of 3manifold mapping class groups, Ohio State University Mathematics Research Institute, March 14, 1990. 
25.  Concentration points for Fuchsian groups, Colloquium at Oklahoma State University, September 27, 1990. 
26.  Concentration points for Fuchsian groups, Special Session on Discrete Groups and Geometric Structures in Dimensions 2, 3, and 4, AMS Regional Meeting, Amherst, Massachusetts, October 21, 1990. 
27.  Geodesic separation points for Fuchsian groups and laminations in surfaces, Special Session on Lowdimensional Topology, AMS Regional Meeting, Denton, Texas, November 2, 1990. 
28.  Weak concentration points for Kleinian groups, Special Session on Lowdimensional Topology and Negatively Curved Groups, AMS Regional Meeting, Santa Barbara, California, November 10, 1991. 
29.  Realizability of automorphisms of 3manifold groups and deformation spaces of Kleinian groups, Special Session on Hyperbolic Manifolds, AMS Regional Meeting, Dayton, Ohio, October 31, 1992. 
30.  Computer estimation of Hausdorff dimension for limit sets of Schottky groups, Workshop on Computational Problems in the Theory of Riemann Surfaces and Related Topics, Tenerife, Spain, December 9, 1992. 
31.  Compression bodies in topology, 3Manifolds Week, Tokyo Institute of Technology, Tokyo, Japan, December 19, 1994. 
32.  Compression bodies in geometry, 3Manifolds Week, Tokyo Institute of Technology, Tokyo, Japan, December 20, 1994. 
33.  Limit sets of Kleinian groups, Colloquium at Okayama University of Science, Okayama, Japan, December 22, 1994. 
34.  Compression bodies in 3dimensional topology (lecture series), Seoul National University, Seoul, Korea, December 2629, 1994. 
35.  Isotopies of 3manifolds, Special Session on Lowdimensional Topology, AMSSMM Second Joint Meeting, Guanajuato, Mexico, December 1, 1995. 
36.  Fiberpreserving diffeomorphisms, Topology Seminar at University of Michigan, Ann Arbor, Michigan, October 17, 1996. 
37.  Conjectures on 3manifold mapping class groups, Lowdimensional Topology Seminar, Mathematical Sciences Research Institute, Berkeley, California, November 21, 1996. 
38.  Diffeomorphisms of 3manifolds, Texas Geometry and Topology Conference, Texas Christian University, Ft. Worth, Texas, February 8, 1997. 
39.  Fiberpreserving diffeomorphisms, Colloquium at Texas Christian University, Ft. Worth, Texas, February 11, 1997. 
40.  The topology of deformation spaces of hyperbolic 3manifolds, Special Session on Lowdimensional Topology, AMSSMM Fourth Joint Meeting, Denton, Texas, May 22, 1999. 
41.  Free actions on handlebodies, Spring Topology and Dynamical Systems Conference, Morelia, Michoacán, Mexico, March 15, 2001. 
42.  Imbedding free actions on handlebodies in free actions on 3manifolds, Special Session on Hyperbolic Manifolds and Discrete Groups, AMS Regional Meeting, Ann Arbor, Michigan, March 3, 2002. 
43.  Group actions on handlebodies, Conference on Conformal Geometry, Discrete Groups and Surfaces, Bedlewo, Poland, June 30, 2003. 
44.  Free actions of finite groups on handlebodies (two lecture series), Anam Lectureship, Korea University, Seoul, Korea, August 56, 2003. 
45.  Free actions on handlebodies, Colloquium at Sogang University, Seoul, Korea, August 8, 2003. 
46.  Diffeomorphisms of lowdimensional manifolds, Colloquium at Oklahoma State University, November 7, 2003. 
47.  Diffeomorphisms of lowdimensional manifolds, Colloquium at Universidade Federal de Pernambuco, Recife, Brazil, February 5, 2004. 
48.  The Smale Conjecture for elliptic 3manifolds, Special Session on Results in 3manifolds and Related Topics, AMS Regional Meeting, Tallahassee, Florida, March 12, 2004. 
49.  The Smale Conjecture for lens spaces, Spring Topology and Dynamics Conference, University of Alabama at Birmingham, Birmingham, Alabama, March 25, 2004. 
50.  Nielsen equivalence, group actions, and PSL(2,q), First ArkansasOklahoma Workshop in Topology and Geometry, Fayetteville, Arkansas, May 19, 2005. 
51.  Nielsen equivalence and PSL(2,q), Colloquium at Texas Christian University, Ft. Worth, Texas, February 14, 2006. 
52.  Nielsen equivalence and PSL(2,q), Colloquium at Oklahoma State University, Stillwater, Oklahoma, March 24, 2006. 
53.  The tree of knot tunnels, Colloquium at University of Arkansas, Fayetteville, Arkansas, November 20, 2006. 
54.  Applications of the disk complex of the genus2 handlebody to knot theory, AMS Special Session on Mapping Class Groups and Handlebodies, Joint Mathematics Meetings, New Orleans, Louisiana, January 8, 2007. 
55.  Parameterizing the set of knot tunnels, Special Session on Geometric Topology and Geometric Group Theory, FortyFirst Annual Spring Topology and Dynamics Conference, University of Missouri at Rolla, Rolla, Missouri, March 30, 2007. 
56.  All tunnels of all tunnel number 1 knots, Geometric Topology Conference, Beijing University, Beijing, China, June 22, 2007. 
57.  Constructing knot tunnels using giant steps, Special Session on Heegaard Splittings, Bridge Number, and Lowdimensional Topology, Joint Mathematics Meetings, San Diego, California, January 9, 2008. 
58.  Heegaard splittings of knot complements, Colloquium at Rice University, Houston, Texas, February 14, 2008. 
59.^{ }  Disk complexes, arc complexes, and knots, 4^{th} William Rowan Hamilton Geometry and Topology Workshop, Trinity College, Dublin, Ireland, August 28, 2008. 
60.  The tunnel leveling addendum, Geometric Topology in 3 and 4 Dimensions, University of California, Davis, California, June 23, 2009. 
61.  Genus2 Heegaard splittings of knot exteriors, and The space of Heegaard splittings, Seminar at Caltech, Pasadena, California, June 11, 2010. 
62.  Diffeomorphisms and Heegaard splittings of 3manifolds, Geometry & Topology Down Under, University of Melbourne, Melbourne, Australia, July 19, 2011. 
Undergraduate Courses Taught:


1.^{ }  An interesting calculus problem, 52^{nd} Annual Meeting of the OklahomaArkansas Section of the MAA, Siloam Springs, AR, March 30, 1990. 
2.^{ }  Symmetries of 3dimensional handlebodies, 53^{rd} Annual Meeting of the OklahomaArkansas Section of the MAA, Lawton, OK, April 5, 1991. 
3.^{ }  A geometric interpretation of continued fractions, 54^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Arkadelphia, AR, April 4, 1992. 
4.^{ }  Euler's evaluation of Σ (1)^{n}n!, 55^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Tulsa, OK, March 27, 1993. 
5.^{ }  Points at odd integral distances, 56^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Searcy, AR, March 25, 1994. 
6.^{ }  A proof that π and e are irrational, 57^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Weatherford, OK, March 31, 1995. 
7.^{ }  1^{k} + 2^{k} + ... + n^{k}, 58^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Ft. Smith, AR, March 22, 1996. 
8.^{ }  A metric for the real line with no connected open balls, 59^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Edmond, OK, April 4, 1997. 
9.^{ }  Two proofs of a theorem of Erdös and Szekeres, 60^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Little Rock, AR, March 27, 1998. 
10.^{ }  The largest compact metric space, 61^{st} Annual Meeting of the OklahomaArkansas Section of the MAA, Bethany, OK, March 27, 1999. 
11.^{ }  Not necessarily algebraic topology, 62^{nd} Annual Meeting of the OklahomaArkansas Section of the MAA, Russellville, AR, April 1, 2000. 
12.^{ }  Complex complex numbers, 63^{rd} Annual Meeting of the OklahomaArkansas Section of the MAA, Oklahoma City, OK, March 31, 2001. 
13.^{ }  Recursive enumeration of Pythagorean triples, 65^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Tulsa, OK, March 28, 2003. 
14.^{ }  Beyond the intermediate value theorem, Anam^{ }Foundation Lecture, Korea University, Seoul, Korea, August 7, 2003. 
15.^{ }  What is f ' ?, 67^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Ada, OK, April 9, 2005. 
16.^{ }  GianCarlo Rota (19321999), Featured Speaker at the 68^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, Fayetteville, AR, April 1, 2006. 
17.^{ }  Learning from my students, 70^{th} Annual Meeting of the OklahomaArkansas Section of the MAA, University of Arkansas Ft. Smith, Ft. Smith, AR, March 29, 2008. 
18.^{ }  On the matrices AB and BA, 72^{nd} Annual Meeting of the OklahomaArkansas Section of the MAA, John Brown University, Siloam Springs, AR, March 27, 2010. 
19.^{ }  A senior mathematics capstone course, 73^{rd} Annual Meeting of the OklahomaArkansas Section of the MAA, University of Central Oklahoma, Edmond, Oklahoma, April 1, 2011. 
Summary of Departmental Service:
1.  Departmental Service and Committes
 
2.  Mathematics doctoral committees: 35
 
3.  Departmental seminars presented: 151 
Summary of University Service:
1.  University Committees
 
2.  Doctoral committees (12): Physics 5 Music 2, Civil Engineering 1, Communication 1; Economics 1, Electrical Engineering 1, Finance 1 
Summary of Professional Service:
As of: February 1, 2014
1.
Referee for journal articles (85):
2.
Reviewer for journal articles (500):
3.
Reviewer for research proposals
4.
MidAmerican State Universities Association Honor Lecturer (198788)
5.
Service to Mathematical Association of America, OklahomaArkansas Section