Towards Ivanov's meta-conjecture for geodesic currents
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913697288421376 |
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| author | Jyothis, Meenakshy |
| author_facet | Jyothis, Meenakshy |
| contents | Given a closed, orientable surface $S$ of negative Euler characteristic, we study two automorphism groups: $Aut(\mathscr{C})$ and $Aut(\mathcal{ML})$, groups of homeomorphisms that preserve the intersection form in the space $\mathscr{C}$ of geodesic currents and the space $\mathcal{ML}$ of measured laminations. We prove that except in a few special cases, $Aut(\mathcal{ML})$ is isomorphic to the extended mapping class group. This theorem is a special case of \textit{Ivanov's meta-conjecture}. We investigate this question for $Aut(\mathscr{C})$. To demonstrate the difficulty in proving Ivanov's conjecture for $Aut(\mathscr{C})$, we construct infinite family of pairs of closed curves that have the simple same marked length spectra and self intersection number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14532 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards Ivanov's meta-conjecture for geodesic currents Jyothis, Meenakshy Geometric Topology Given a closed, orientable surface $S$ of negative Euler characteristic, we study two automorphism groups: $Aut(\mathscr{C})$ and $Aut(\mathcal{ML})$, groups of homeomorphisms that preserve the intersection form in the space $\mathscr{C}$ of geodesic currents and the space $\mathcal{ML}$ of measured laminations. We prove that except in a few special cases, $Aut(\mathcal{ML})$ is isomorphic to the extended mapping class group. This theorem is a special case of \textit{Ivanov's meta-conjecture}. We investigate this question for $Aut(\mathscr{C})$. To demonstrate the difficulty in proving Ivanov's conjecture for $Aut(\mathscr{C})$, we construct infinite family of pairs of closed curves that have the simple same marked length spectra and self intersection number. |
| title | Towards Ivanov's meta-conjecture for geodesic currents |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2309.14532 |