On fixed points of pseudo-Anosov maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917409057669120 |
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| author | Aougab, Tarik Futer, David Taylor, Samuel J. |
| author_facet | Aougab, Tarik Futer, David Taylor, Samuel J. |
| contents | We give a formula to estimate the number of fixed points of a pseudo-Anosov homeomorphism of a surface. When the homeomorphism satisfies a mild property called strong irreducibility, the log of the number of fixed points is coarsely equal to the Teichmuller translation length. We also discuss several applications, including an inequality relating the hyperbolic volume of a mapping torus to the rank of its Heegaard Floer homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On fixed points of pseudo-Anosov maps Aougab, Tarik Futer, David Taylor, Samuel J. Geometric Topology Dynamical Systems Group Theory 57K20, 37E30 (primary), 57K32, 57K18 (secondary) We give a formula to estimate the number of fixed points of a pseudo-Anosov homeomorphism of a surface. When the homeomorphism satisfies a mild property called strong irreducibility, the log of the number of fixed points is coarsely equal to the Teichmuller translation length. We also discuss several applications, including an inequality relating the hyperbolic volume of a mapping torus to the rank of its Heegaard Floer homology. |
| title | On fixed points of pseudo-Anosov maps |
| topic | Geometric Topology Dynamical Systems Group Theory 57K20, 37E30 (primary), 57K32, 57K18 (secondary) |
| url | https://arxiv.org/abs/2509.07818 |