# On the stable Cannon Conjecture

Presented by:
Wolfgang Lueck Universität Bonn
Date:
Tuesday 4th December 2018 - 09:00 to 10:00
Venue:
INI Seminar Room 1
Abstract:
The Cannon Conjecture for a torsionfree hyperbolic group $G$ with boundary homeomorphic to $S^2$ says that $G$ is the fundamental group of an aspherical closed $3$-manifold $M$.  It is known that then $M$ is a hyperbolic $3$-manifold.  We prove the stable version that for any closed manifold $N$ of dimension greater or equal to $2$  there exists a closed manifold $M$ together with a simple homotopy equivalence $M \to N \times BG$. If $N$ is aspherical and $\pi_1(N)$ satisfies the Farrell-Jones Conjecture, then $M$ is unique up to homeomorphism.
This is joint work with Ferry and Weinberger.
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