Exam I will be in Room 809 PHSC on Tuesday, May 10, 2005, from 1:30-3:30 p. m. Its emphasis is on the classification theorem for surfaces, Euler characteristic, the compact-open topology, and the theory of covering spaces. The topics include (but are not limited to) the following:

1.	Invariance of Domain
2.	The classification of compact, connected surfaces. The use of the Euler characteristic formula χ(S2 # gT # nP # kD) = 2 - 2g - n - k.
3.	The connected sum operation for surfaces.
4.	The compact-open topology.
5.	Simply-connected spaces.
6.	Basic covering space theory. The Lifting Criterion. Lifting paths and loops to covering spaces.

The following topics will not appear on the exam:

1.	Isotopy of homeomorphisms, ambient isotopy
2.	Handle-decompositions and handle sliding, the Disk Lemma
3.	Verification of the group properties of &pi1(X,x0).
4.	[Sm,Sn], degree of maps between spheres, degree of maps from S1 to S1, Fundamental Theorem of Algebra
5.	Barycentric subdivision, triangulations of surfaces
6.	Details of complicated proofs, such as continuity of the lift in the proof of the Lifting Theorem.