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On the stable Cannon Conjecture

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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 $M o N imes BG$. 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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