The twist-cofinite topology on the mapping class group of a surface
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913975125409792 |
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| author | Irmer, Ingrid |
| author_facet | Irmer, Ingrid |
| contents | A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this notion easily; for example, the set of pseudo-Anosov maps is shown to be generic, and can be assumed to have arbitrary large stretch factor, generically. Let M be a 3-manifold obtained from a Heegaard splitting of fixed genus g and generic gluing map. It is shown that for such manifolds, generically M is hyperbolic, has first Betti number zero and Heegaard genus exactly equal to g. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_11212 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The twist-cofinite topology on the mapping class group of a surface Irmer, Ingrid Geometric Topology Group Theory A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this notion easily; for example, the set of pseudo-Anosov maps is shown to be generic, and can be assumed to have arbitrary large stretch factor, generically. Let M be a 3-manifold obtained from a Heegaard splitting of fixed genus g and generic gluing map. It is shown that for such manifolds, generically M is hyperbolic, has first Betti number zero and Heegaard genus exactly equal to g. |
| title | The twist-cofinite topology on the mapping class group of a surface |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2003.11212 |