Mathematical Research Letters

Volume 13 (2006)

Number 6

Countable groups are mapping class groups of hyperbolic $3$-manifolds

Pages: 897 – 910

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n6.a5

Authors

Roberto Frigerio

Bruno Martelli

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 $\pi_1 (M)$ are isomorphic to $G$.

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