Extensions of Veech groups I: A hyperbolic action
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913256802615296 |
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| author | Dowdall, Spencer Durham, Matthew G. Leininger, Christopher J. Sisto, Alessandro |
| author_facet | Dowdall, Spencer Durham, Matthew G. Leininger, Christopher J. Sisto, Alessandro |
| contents | Given a lattice Veech group in the mapping class group of a closed surface $S$, this paper investigates the geometry of $Γ$, the associated $π_1S$--extension group. We prove that $Γ$ is the fundamental group of a bundle with a singular Euclidean-by-hyperbolic geometry. Our main result is that collapsing "obvious" product regions of the universal cover produces an action of $Γ$ on a hyperbolic space, retaining most of the geometry of $Γ$. This action is a key ingredient in the sequel where we show that $Γ$ is hierarchically hyperbolic and quasi-isometrically rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_16425 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Extensions of Veech groups I: A hyperbolic action Dowdall, Spencer Durham, Matthew G. Leininger, Christopher J. Sisto, Alessandro Geometric Topology Group Theory 20F67, 20F65, 30F60, 57M60, 57M07 Given a lattice Veech group in the mapping class group of a closed surface $S$, this paper investigates the geometry of $Γ$, the associated $π_1S$--extension group. We prove that $Γ$ is the fundamental group of a bundle with a singular Euclidean-by-hyperbolic geometry. Our main result is that collapsing "obvious" product regions of the universal cover produces an action of $Γ$ on a hyperbolic space, retaining most of the geometry of $Γ$. This action is a key ingredient in the sequel where we show that $Γ$ is hierarchically hyperbolic and quasi-isometrically rigid. |
| title | Extensions of Veech groups I: A hyperbolic action |
| topic | Geometric Topology Group Theory 20F67, 20F65, 30F60, 57M60, 57M07 |
| url | https://arxiv.org/abs/2006.16425 |