Mathematical Research Letters

Volume 13, Issue 6, November 2006 pp. 897-910.

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

Authors: Roberto Frigerio and Bruno Martelli
Author institution: Università di Pisa

Summary: 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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