The Goeritz groups of $(1,1)$-decompositions

Yuya Koda; Yuki Tanaka

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arXiv · 2403.15809

The Goeritz groups of $(1,1)$-decompositions

Yuya Koda·Yuki Tanaka

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Abstract

A $(g, n)$-decomposition of a link $L$ in a closed orientable $3$-manifold $M$ is a decomposition of $M$ by a closed orientable surface of genus $g$ into two handebodies each intersecting the link $L$ in $n$ trivial arcs. The Goeritz group of that decomposition is then defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the pair $(M, L)$ that preserve the decomposition. We compute the Goeritz groups of all $(1,1)$-decompositions.

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Yuya Koda, Yuki Tanaka. 2024-03-23. The Goeritz groups of $(1,1)$-decompositions. https://arxiv.org/abs/2403.15809

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