The quadric flat torus theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914585816072192 |
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| author | Hoda, Nima Munro, Zachary |
| author_facet | Hoda, Nima Munro, Zachary |
| contents | We prove a flat torus theorem for quadric complexes. In particular, we show that if a non-cyclic free abelian group $G$ acts metrically properly on a quadric complex $X$, then $G \cong \mathbb{Z}^2$ and $X$ contains a $G$-invariant isometric copy of the regular square tiling of the plane.
Along the way, we also give a complete proof of the fact that any closed surface subgroup in the fundamental group of a combinatorial 2-complex is represented by a combinatorial map from a cellulation of the surface that is locally injective away from vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quadric flat torus theorem Hoda, Nima Munro, Zachary Group Theory Combinatorics 20F65, 20F67 We prove a flat torus theorem for quadric complexes. In particular, we show that if a non-cyclic free abelian group $G$ acts metrically properly on a quadric complex $X$, then $G \cong \mathbb{Z}^2$ and $X$ contains a $G$-invariant isometric copy of the regular square tiling of the plane. Along the way, we also give a complete proof of the fact that any closed surface subgroup in the fundamental group of a combinatorial 2-complex is represented by a combinatorial map from a cellulation of the surface that is locally injective away from vertices. |
| title | The quadric flat torus theorem |
| topic | Group Theory Combinatorics 20F65, 20F67 |
| url | https://arxiv.org/abs/2410.09905 |