An Overview of Relative Trisections

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. Non UBCUnreviewedAuthor affiliation: University of GeorgiaPostdoctora