Patrick Naylor, Department of Pure Mathematics, University of Waterloo
"Trisections of non-orientable 4—manifolds"
One highly useful such tool is the notion of a Heegaard splitting: a decomposition of a 3—manifold into two equal pieces. In analogy with this decomposition, Gay and Kirby recently defined the notion of a trisection of a closed oriented 4—manifold: it is a similar decomposition, but into three equal pieces. Trisections provide a novel diagrammatic perspective on 4—manifolds, and have already been used to define new invariants and reprove fundamental results in gauge theory.
In this talk, I will discuss my thesis (based on a joint project with Maggie Miller), which extends these decompositions to non-orientable 4—manifolds. In particular, we prove a non-orientable analogue of a theorem of Laudenbach-Poénaru that does not seem to appear in the literature, and is critical for descriptions of closed non-orientable 4—manifolds. We also give a non-orientable analogue of a theorem of Waldhausen on Heegaard splitting off #S^2xS1. The talk will begin with a brief introduction to the theory of trisections, and then highlight the differences in the non-orientable setting.
Please contact Nancy Maloney (email@example.com) if you are interested in virtually attending Patrick's talk.