A PL approach to trisections of 4-manifolds through colored triangulations
speaker: Paola Cristofori (Università di Modena e Reggio Emilia)abstract: According to Gay and Kirby a trisection of a smooth, oriented, closed 4-manifold M is a decomposition of M into three 4-dimensional handlebodies mutually intersecting in 3-dimensional handlebodies and globally intersecting in a closed orientable surface. The minimum genus of the intersecting surface is called the trisection genus of M. In this talk, by taking advantage of the coincidence between PL and DIFF categories in dimension 4, we describe a PL approach to trisections realized through edge-colored graphs (gems) encoding colored triangulations. The constructions can also be easily extended so as to include manifolds with connected boundary and non-orientable ones; furthermore PL analogues of trisections and trisection genus can be defined and studied directly on gems. As a consequence, we prove that the graph-defined PL invariant regular genus provides an upper bound for the value of the trisection genus of each closed 4-manifold; for particular classes of manifolds we are also able to realize the trisection genus via gems. Moreover, we will present an estimation of the trisection genus of any closed orientable 4-manifold in terms of the properties of a Kirby diagram. The talk is based on joint works with M.R. Casali.
timetable:
Thu 3 Oct, 14:30 - 15:30, Aula Dini
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