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Countable groups are mapping class groups of hyperbolic 3-manifolds

Roberto Frigerio·Bruno Martelli
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Abstract

We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.

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Roberto Frigerio, Bruno Martelli. 2005-09-14. Countable groups are mapping class groups of hyperbolic 3-manifolds. https://arxiv.org/abs/math/0509311

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