Quadratic-time computations for pseudo-Anosov mapping classes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911729841078272 |
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| author | Margalit, Dan Strenner, Balázs Taylor, Samuel J. Yurttaş, S. Öykü |
| author_facet | Margalit, Dan Strenner, Balázs Taylor, Samuel J. Yurttaş, S. Öykü |
| contents | We give a quadratic-time algorithm to compute the stretch factor and the invariant measured foliations for a pseudo-Anosov element of the mapping class group. As input, the algorithm accepts a word (in any given finite generating set for the mapping class group) representing a pseudo-Anosov mapping class, and the length of the word is our measure of complexity for the input. The output is a train track and an integer matrix where the stretch factor is the largest real eigenvalue and the unstable foliation is given by the corresponding eigenvector. This is the first algorithm to compute stretch factors and measured foliations that is known to terminate in sub-exponential time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic-time computations for pseudo-Anosov mapping classes Margalit, Dan Strenner, Balázs Taylor, Samuel J. Yurttaş, S. Öykü Geometric Topology Dynamical Systems 57K20 We give a quadratic-time algorithm to compute the stretch factor and the invariant measured foliations for a pseudo-Anosov element of the mapping class group. As input, the algorithm accepts a word (in any given finite generating set for the mapping class group) representing a pseudo-Anosov mapping class, and the length of the word is our measure of complexity for the input. The output is a train track and an integer matrix where the stretch factor is the largest real eigenvalue and the unstable foliation is given by the corresponding eigenvector. This is the first algorithm to compute stretch factors and measured foliations that is known to terminate in sub-exponential time. |
| title | Quadratic-time computations for pseudo-Anosov mapping classes |
| topic | Geometric Topology Dynamical Systems 57K20 |
| url | https://arxiv.org/abs/2408.07596 |