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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.17047 |
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Table of 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.