# Topological rigidity and low dimensional topology

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Speaker:
Jim Davis
Affiliation:
Bloomington/MPIM
Date:
Mon, 2021-04-26 14:00 - 15:00
Parent event:
MPIM Topology Seminar
An aspherical manifold is a manifold whose universal cover is contractible, i.e. a $K(\pi,1)$-manifold. Borel conjectured that any two closed aspherical manifolds with isomorphic fundamental groups are homeomorphic, in fact, that the structure set of an aspherical manifold is trivial. Wall asked if a $K(\pi,1)$-space which satisfies Poincare duality is homotopy equivalent to a closed manifold. There are corresponding conjectures for compact aspherical manifolds with boundary.

We will survey these topological rigidity conjectures, their relationship with low-dimensional topology, and eventually focus on the questions: What closed 3-manifolds are the boundary of some compact aspherical 4-manifold? What are the fundamental groups of compact aspherical 4-manifolds?

This is the final talk in the following series.

Series title: Applied surgery
Series abstract: Surgery is the key tool for classifying manifolds, up to homeomorphism or diffeomorphism.  This sequence of talks will give an introduction to this tool, and then apply it to specific questions in four manifold topology.

Meeting ID: 916 5855 1117