Entropy versus volume via Heegaard diagrams
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910516947976192 |
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| author | Liu, Yi |
| author_facet | Liu, Yi |
| contents | The following inequalities are established, improving a former inequality due to Kojima. For any closed arithmetic hyperbolic $3$--manifold fibering over a circle, the entropy of the pseudo-Anosov monodromy is bounded by the hyperbolic volume of the $3$--manifold, up to a universal constant factor. For any closed hyperbolic $3$--manifold fibering over a circle with systole $\geq\varepsilon>0$, the entropy is bounded by the hyperbolic volume times $\log(3+1/\varepsilon)$, up to a universal constant factor. The proof relies on Heegaard Floer homology and hyperbolic geometry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_14255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropy versus volume via Heegaard diagrams Liu, Yi Geometric Topology Primary 57K32, 57K20, Secondary 57K18 The following inequalities are established, improving a former inequality due to Kojima. For any closed arithmetic hyperbolic $3$--manifold fibering over a circle, the entropy of the pseudo-Anosov monodromy is bounded by the hyperbolic volume of the $3$--manifold, up to a universal constant factor. For any closed hyperbolic $3$--manifold fibering over a circle with systole $\geq\varepsilon>0$, the entropy is bounded by the hyperbolic volume times $\log(3+1/\varepsilon)$, up to a universal constant factor. The proof relies on Heegaard Floer homology and hyperbolic geometry. |
| title | Entropy versus volume via Heegaard diagrams |
| topic | Geometric Topology Primary 57K32, 57K20, Secondary 57K18 |
| url | https://arxiv.org/abs/2312.14255 |