Open Collections

An Overview of Relative Trisections

Banff International Research Station for Mathematical Innovation and Discovery

Based on the notion of trisections of closed 4--manifolds of Gay and Kirby, Nick Castro and myself developed a rigorous definition of relative trisections as a generalization of trisections to 4--manifolds with boundary. In the talk I will present the basics of relative trisections starting with their relationship to open book decompositions of the bounding manifolds. I will then introduce a stabilization operation that gives rise to a statement about the uniqueness of relative trisections, thus complementing Gay and Kirby's proof of the existence of relative trisections. Finally, I will introduce the notion of diagrams of relative trisections and describe a method to recover the open book decomposition of the bounding manifold from the trisection diagrams. 

Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology

video/mp4

Author affiliation: University of Georgia

2016-08-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58962

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/