Hyperbolic Integral Homology Spheres and Binary Icosahedral Representations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929707058987008 |
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| author | Stuebner, Maria |
| author_facet | Stuebner, Maria |
| contents | This paper examines the representations of hyperbolic integral homology spheres into the binary icosahedral group $2I$. We specifically give a geometric meaning to $2I$ representations by relating them to Larsen's notion of quotient dimension, which gives us a sense of the frequency of regular finite covers. Our main theorem shows that hyperbolic 3-manifolds can only have quotient dimension 2 or 3, and each case is obtained infinitely many times. More specifically, we show that those with no non-trivial $A_5$ representations have quotient dimension 3, and we find a family of hyperbolic 3-manifolds obtained by Dehn surgery on an infinite 2-bridge hyperbolic knot family with quotient dimension 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolic Integral Homology Spheres and Binary Icosahedral Representations Stuebner, Maria Geometric Topology This paper examines the representations of hyperbolic integral homology spheres into the binary icosahedral group $2I$. We specifically give a geometric meaning to $2I$ representations by relating them to Larsen's notion of quotient dimension, which gives us a sense of the frequency of regular finite covers. Our main theorem shows that hyperbolic 3-manifolds can only have quotient dimension 2 or 3, and each case is obtained infinitely many times. More specifically, we show that those with no non-trivial $A_5$ representations have quotient dimension 3, and we find a family of hyperbolic 3-manifolds obtained by Dehn surgery on an infinite 2-bridge hyperbolic knot family with quotient dimension 2. |
| title | Hyperbolic Integral Homology Spheres and Binary Icosahedral Representations |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2502.06488 |