Entropy-Minimizing Diffeomorphisms on a $G_2$-Manifold
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917278239424512 |
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| author | Thakar, Ollie |
| author_facet | Thakar, Ollie |
| contents | In this paper, we construct infinitely many diffeomorphisms of a Joyce manifold $M$ which achieve Yomdin's homological lower bound for topological entropy, imitating a recent construction of Farb-Looijenga for K3 surfaces. Moreover, following a recent paper by Crowley-Goette-Hertl, we show these diffeomorphisms act freely on a connected component of the Teichmüller space of $G_2$ structures on $M$, and hence that the homotopy moduli space of $G_2$ structures on $M$ has infinite fundamental group. We also discuss a putative analogy between dynamics on a $G_2$ manifold and that of an algebraic surface, and prove a theorem about its limitations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07204 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropy-Minimizing Diffeomorphisms on a $G_2$-Manifold Thakar, Ollie Differential Geometry Dynamical Systems Geometric Topology 37B40, 53C29 In this paper, we construct infinitely many diffeomorphisms of a Joyce manifold $M$ which achieve Yomdin's homological lower bound for topological entropy, imitating a recent construction of Farb-Looijenga for K3 surfaces. Moreover, following a recent paper by Crowley-Goette-Hertl, we show these diffeomorphisms act freely on a connected component of the Teichmüller space of $G_2$ structures on $M$, and hence that the homotopy moduli space of $G_2$ structures on $M$ has infinite fundamental group. We also discuss a putative analogy between dynamics on a $G_2$ manifold and that of an algebraic surface, and prove a theorem about its limitations. |
| title | Entropy-Minimizing Diffeomorphisms on a $G_2$-Manifold |
| topic | Differential Geometry Dynamical Systems Geometric Topology 37B40, 53C29 |
| url | https://arxiv.org/abs/2602.07204 |