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

Brandy Doleshal; Matt Rathbun

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

Geometric Topology 2026-02-19 v1

Authors: Brandy Doleshal , Matt Rathbun

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.

Keywords

Goeritz group lens spaces Heegaard splitting homology homotopy

Cite

@article{arxiv.2602.16458,
  title  = {Genus two Goeritz equivalence in lens spaces $L(p,1)$},
  author = {Brandy Doleshal and Matt Rathbun},
  journal= {arXiv preprint arXiv:2602.16458},
  year   = {2026}
}

Comments

25 pages, 15 figures

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