Minimal complexity cusped hyperbolic 3-manifolds with geodesic boundary
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916917898379264 |
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| author | Ekanayake, Anuradha Forester, Max Miller, Nicholas |
| author_facet | Ekanayake, Anuradha Forester, Max Miller, Nicholas |
| contents | In the early 2000s, Frigerio, Martelli, and Petronio studied $3$-manifolds of smallest combinatorial complexity that admit hyperbolic structures. As part of this work they defined and studied the class $M_{g,k}$ of smallest complexity manifolds having $k$ torus cusps and connected totally geodesic boundary a surface of genus $g$. In this paper, we provide a complete classification of the manifolds in $M_{k,k}$ and $M_{k+1,k}$, which are the cases when the genus $g$ is as small as possible. In addition to classifying manifolds in $M_{k,k}$, $M_{k+1,k}$, we describe their isometry groups as well as a relationship between these two sets via Dehn filling on small slopes. Finally, we give a description of important commensurability invariants of the manifolds in $M_{k,k}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal complexity cusped hyperbolic 3-manifolds with geodesic boundary Ekanayake, Anuradha Forester, Max Miller, Nicholas Geometric Topology In the early 2000s, Frigerio, Martelli, and Petronio studied $3$-manifolds of smallest combinatorial complexity that admit hyperbolic structures. As part of this work they defined and studied the class $M_{g,k}$ of smallest complexity manifolds having $k$ torus cusps and connected totally geodesic boundary a surface of genus $g$. In this paper, we provide a complete classification of the manifolds in $M_{k,k}$ and $M_{k+1,k}$, which are the cases when the genus $g$ is as small as possible. In addition to classifying manifolds in $M_{k,k}$, $M_{k+1,k}$, we describe their isometry groups as well as a relationship between these two sets via Dehn filling on small slopes. Finally, we give a description of important commensurability invariants of the manifolds in $M_{k,k}$. |
| title | Minimal complexity cusped hyperbolic 3-manifolds with geodesic boundary |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.18524 |