Rational Hyperbolicity Problem: Part 2.

event Wednesday, September 10, 2025
access_time 4:00pm (CDT)
room PHSC 1105
free_breakfast Tea at 3:30pm (CDT) in PHSC 424

Abstract: We reformulate the conjecture by Grove, Wilking and Yeager, discussed in Part 1, in the more general setting of Singular Riemannian Foliations. Using the methods of Morse Theory, we are able to prove that, under additional hypothesis, the conjecture holds true. In particular, we consider a Singular Riemannian Foliation \((M,\mathcal{F})\) of codimension two on a closed, simply connected manifold \(M\), such that the leaf space \(M/\mathcal{F}\) supports a metric of hyperbolic type. If we also require that the multiplicities of the sides of \(M/\mathcal{F}\), which count the dimensional drop of the leaves, are strictly greater than one, then \(M\) is rationally hyperbolic. More precisely, we show that rational hyperbolicity is a consequence of the orientability of certain iterated sphere bundles called Bott-Samelson cycles. In turn, the orientability of such cycles follows from the condition on the multiplicities. This is a joint work with Professor M. Radeschi and Professor R. Mendes.


For more information on this event, please contact Nicholas Miller.