Mapping classes of Real Rational Surface Automorphisms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914014653579264 |
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| author | Kim, Kyounghee |
| author_facet | Kim, Kyounghee |
| contents | Let $\{F_n, n\ge 8\}$ be a family of diffeomorphisms on real rational surfaces that are birationally equivalent to birational maps on $\mathbf{P}^2(\mathbb{R})$. In this article, we investigate the mapping classes of the diffeomorphisms $F_n, n\ge 8$. These diffeomorphisms are reducible with unique invariant irreducible curves, and we determine the mapping classes of their restrictions, $\hat F_n, n \ge 8$, on the cut surfaces, showing that they are pseudo-Anosov and do not arise from Penner's construction. For $n=8$, Lehmer's number is realized as the stretch factor of $\hat F_8$, a pseudo-Anosov map on a once-punctured genus $5$ orientable surface. The diffeomorphism $\hat F_8$ is a new geometric realization of a Lehmer's number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mapping classes of Real Rational Surface Automorphisms Kim, Kyounghee Dynamical Systems Geometric Topology 37E30, 57K20, 37F99, 14E07 Let $\{F_n, n\ge 8\}$ be a family of diffeomorphisms on real rational surfaces that are birationally equivalent to birational maps on $\mathbf{P}^2(\mathbb{R})$. In this article, we investigate the mapping classes of the diffeomorphisms $F_n, n\ge 8$. These diffeomorphisms are reducible with unique invariant irreducible curves, and we determine the mapping classes of their restrictions, $\hat F_n, n \ge 8$, on the cut surfaces, showing that they are pseudo-Anosov and do not arise from Penner's construction. For $n=8$, Lehmer's number is realized as the stretch factor of $\hat F_8$, a pseudo-Anosov map on a once-punctured genus $5$ orientable surface. The diffeomorphism $\hat F_8$ is a new geometric realization of a Lehmer's number. |
| title | Mapping classes of Real Rational Surface Automorphisms |
| topic | Dynamical Systems Geometric Topology 37E30, 57K20, 37F99, 14E07 |
| url | https://arxiv.org/abs/2407.15075 |