Genus two Goeritz equivalence in lens spaces $L(p,1)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| author | Doleshal, Brandy Rathbun, Matt |
| author_facet | Doleshal, Brandy Rathbun, Matt |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Genus two Goeritz equivalence in lens spaces $L(p,1)$ Doleshal, Brandy Rathbun, Matt Geometric Topology 57K20, 57S25, 57K10, 57M60 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. |
| title | Genus two Goeritz equivalence in lens spaces $L(p,1)$ |
| topic | Geometric Topology 57K20, 57S25, 57K10, 57M60 |
| url | https://arxiv.org/abs/2602.16458 |