University of Arkansas Topology Seminar: 4/26/2018

Speaker: Nick Castro

Title: Relative trisections and induced monodromies

A relative trisection of a smooth, compact, connected, oriented 4–manifold with non-empty boundary is a decomposition into three codimension zero subspaces whose triple intersection is a surface with boundary and whose pairwise intersections are specific types of cobordisms between surface. Given a relative trisection, the bounding 3–manifold inherits the structure of an open book decomposition. In joint work with Gay and Pinzón, an explicit algorithm was given to recover the (abstract) open book from a relative trisection diagram. In this talk, we will use this algorithm to explore the complexity of the monodromy of an induced open book decomposition. This gives rise to interesting questions regarding relatively trisected cobordisms and their induced open books.