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Graduate Student Geometry-Topology Seminar

Monday, March 27, 2017 - 3:15pm

Simon Lohove

University of Pennsylvania


University of Pennsylvania


The idea behind trisections is to generalize Heegaard splittings of 3-manifolds, which are decompositions in two 3-dimensional handlebodies, to 4-manifolds. In fact, it is always possible to decompose an oriented 4-manifold into three 4-dimensional handlebodies. After a short introduction to the basic notions regarding trisections, we will see some examples and state the main theorem developed so far in this theory (by Abrams, Gay, and Kirby): closed oriented smooth 4-manifolds, up to diffeomorphisms, are in one-to-one correspondence with trisection diagrams, up to a certain equivalence relation.