Thesis Defense
Wednesday August 14th, 2019
Time: 2:00 PM
Title: The Yamabe invariant of Inoue surfaces and their blowups
Speaker: Michael Albanese, Stony Brook University
Location: Math Tower P-131
Abstract:
The Yamabe invariant of a closed smooth manifold is a real-valued diffeomorphism invariant coming from Riemannian geometry. Using Seiberg-Witten theory, LeBrun showed that the sign of the Yamabe invariant of a Kähler surface is determined by its Kodaira dimension, a complex-geometric invariant of the surface. It is not hard to see that the simplest non-Kähler surfaces, namely Hopf surfaces and their blowups, follow the pattern laid out by LeBrun's theorem. However, we will show that the non-Kähler analogue of LeBrun's theorem does not hold. In particular, we prove that the Yamabe invariants of Inoue surfaces and their blowups are all zero. This is achieved by developing a result which rules out the existence of positive scalar curvature metrics on a larger class of examples.