Automorphisms of the compression body graph

Abstract

When $S$ is a closed, orientable surface with genus $g(S)\ge 2$, we show that the automorphism group of the compression body graph $\mathcal{CB}(S)$ is the mapping class group. Here, vertices are compression bodies with exterior boundary $S$, and edges connect pairs of compression bodies where one contains the other.

25 pages, 10 figures

Cited by in corpus (5)

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• Thick hyperbolic 3-manifolds with bounded rank
• Extending powers of pseudo-Anosovs
• Asymptotic dimensions of the arc graphs and disk graphs
• Heegaard distance of the link complements in $S^3$