A smooth Birman-Hilden theory for hyperkähler manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929692810936320 |
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| author | Raman, Sidhanth |
| author_facet | Raman, Sidhanth |
| contents | This article grew out of an effort to understand the smooth mapping class groups of certain 4-manifolds in a geometric manner. We prove a smooth analog of the Birman-Hilden theorem for manifolds that admit a hyperkähler structure. This allows us to probe the smooth mapping class groups associated to certain manifolds with nontrivial fundamental groups. Along the way, and of independent interest, we prove a global Torelli theorem for generalized Enriques manifolds. The techniques used are analogous to Teichmüller-theoretic methods in the classical theory of mapping class groups. We apply this hyperkähler Birman-Hilden theorem to obtain results regarding smooth, metric, and complex Nielsen realization on Enriques surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A smooth Birman-Hilden theory for hyperkähler manifolds Raman, Sidhanth Geometric Topology Algebraic Geometry This article grew out of an effort to understand the smooth mapping class groups of certain 4-manifolds in a geometric manner. We prove a smooth analog of the Birman-Hilden theorem for manifolds that admit a hyperkähler structure. This allows us to probe the smooth mapping class groups associated to certain manifolds with nontrivial fundamental groups. Along the way, and of independent interest, we prove a global Torelli theorem for generalized Enriques manifolds. The techniques used are analogous to Teichmüller-theoretic methods in the classical theory of mapping class groups. We apply this hyperkähler Birman-Hilden theorem to obtain results regarding smooth, metric, and complex Nielsen realization on Enriques surfaces. |
| title | A smooth Birman-Hilden theory for hyperkähler manifolds |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2402.17047 |