Genus two Goeritz equivalence in lens spaces $L(p,1)$

Brandy Doleshal; Matt Rathbun

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arXiv · 2602.16458

Genus two Goeritz equivalence in lens spaces $L(p,1)$

Brandy Doleshal·Matt Rathbun

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Abstract

In this paper, we consider the action of the Goeritz group $\mathcal G_p$ for the genus two Heegaard splitting of the lens space $L(p,1)$ with $p\ge 2$ on the homology of the Heegaard surface. We describe the action in terms of matrices in $GL(4, \mathbb Z)$, and provide homology and homotopy obstructions for when two curves in the Heegaard surface are Goeritz equivalent.

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Brandy Doleshal, Matt Rathbun. 2026-02-18. Genus two Goeritz equivalence in lens spaces $L(p,1)$. https://arxiv.org/abs/2602.16458

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