Coning off totally geodesic boundary components of a hyperbolic manifold
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915751404765184 |
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| author | Kelln, Colby Manning, Jason |
| author_facet | Kelln, Colby Manning, Jason |
| contents | Let M be a compact hyperbolic manifold with totally geodesic boundary. If the injectivity radius of the boundary is larger than an explicit function of the normal injectivity radius of the boundary, we show that there is a negatively curved metric on the space obtained by coning each boundary component of M to a point. Moreover, we give explicit geometric conditions under which a locally convex subset of M gives rise to a locally convex subset of the cone-off.
Group-theoretically, we conclude that the fundamental group of the cone-off is hyperbolic and the image of the fundamental group of the coned-off locally convex subset is a quasi-convex subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coning off totally geodesic boundary components of a hyperbolic manifold Kelln, Colby Manning, Jason Geometric Topology Group Theory Let M be a compact hyperbolic manifold with totally geodesic boundary. If the injectivity radius of the boundary is larger than an explicit function of the normal injectivity radius of the boundary, we show that there is a negatively curved metric on the space obtained by coning each boundary component of M to a point. Moreover, we give explicit geometric conditions under which a locally convex subset of M gives rise to a locally convex subset of the cone-off. Group-theoretically, we conclude that the fundamental group of the cone-off is hyperbolic and the image of the fundamental group of the coned-off locally convex subset is a quasi-convex subgroup. |
| title | Coning off totally geodesic boundary components of a hyperbolic manifold |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2504.21652 |