On the stable Cannon Conjecture

Steve Ferry; Wolfgang Lueck; Shmuel Weinberger

doi:10.1112/topo.12099

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arXiv · 1804.00738

On the stable Cannon Conjecture

Steve Ferry·Wolfgang Lueck·Shmuel Weinberger

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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 from M to the cartesian product of N and BG. If N is aspherical and pi_1(N) satisfies the Farrell-Jones Conjecture, then M is unique up to homeomorphism.

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Steve Ferry, Wolfgang Lueck, Shmuel Weinberger. 2019-03-17. On the stable Cannon Conjecture. https://doi.org/10.1112/topo.12099

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