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Group trisections and smooth four-manifolds

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Jeffrey Lee Meier
Indiana U. / HCM
Mon, 12/12/2016 - 16:30 - 18:00
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In this talk, I will introduce the notion of a trisection of a group, and I'll explain how studying group trisections is equivalent to studying smooth structures on 4-manifolds.

The proof of this striking theorem, which is the main result of a recent eponymous paper by Abrams, Gay, and Kirby, involves a straightforward and beautiful synthesis of foundational theorems from the theories of 2-, 3-, and 4-dimensional manifolds. After presenting the proof, I will conclude by discussing connections to the Poincare Conjecture, Andrews-Curtis Conjecture, and knotted surface theory.

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