A survey on mapping class groups of 3-manifolds

Philipp Bader; Rachael Boyd; Giulia Carfora; Gabriel Corrigan; Daniel Galvin; Csaba Nagy; John Nicholson; Weizhe Niu; Isacco Nonino; Mark Pencovitch; Mark Powell

arXiv · 2609.00233

A survey on mapping class groups of 3-manifolds

Philipp Bader·Rachael Boyd·Giulia Carfora·Gabriel Corrigan·Daniel Galvin·Csaba Nagy·John Nicholson·Weizhe Niu·Isacco Nonino·Mark Pencovitch·Mark Powell

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Abstract

We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold $M$. We provide a guide to the literature and sketch proofs for various families of irreducible and geometric 3-manifolds. We also consider JSJ and prime decompositions of 3-manifolds, and consequences for their mapping class groups.

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Philipp Bader, Rachael Boyd, Giulia Carfora, Gabriel Corrigan, Daniel Galvin, Csaba Nagy, John Nicholson, Weizhe Niu, Isacco Nonino, Mark Pencovitch, Mark Powell. 2026-08-31. A survey on mapping class groups of 3-manifolds. https://arxiv.org/abs/2609.00233

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