Euclidean lengths and the Culler-Shalen norms of slopes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912709873762304 |
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| author | Ichihara, Kazuhiro |
| author_facet | Ichihara, Kazuhiro |
| contents | In the study of exceptional Dehn fillings, two functions on slopes, called the Euclidean length on a horotorus and the Culler-Shalen norm, play important roles. In this paper, we investigate their relationship and establish two inequalities between them. As a byproduct, some bounds on the boundary slope diameter are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euclidean lengths and the Culler-Shalen norms of slopes Ichihara, Kazuhiro Geometric Topology Primary 57K32, Secondary 57K10 In the study of exceptional Dehn fillings, two functions on slopes, called the Euclidean length on a horotorus and the Culler-Shalen norm, play important roles. In this paper, we investigate their relationship and establish two inequalities between them. As a byproduct, some bounds on the boundary slope diameter are given. |
| title | Euclidean lengths and the Culler-Shalen norms of slopes |
| topic | Geometric Topology Primary 57K32, Secondary 57K10 |
| url | https://arxiv.org/abs/2507.09986 |