Knot exteriors with all compact surfaces of positive genus essentially embedded
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916914616336384 |
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| author | Nogueira, Joao M. |
| author_facet | Nogueira, Joao M. |
| contents | It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knot exteriors with all compact surfaces of positive genus essentially embedded Nogueira, Joao M. Geometric Topology 57K10 It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components. |
| title | Knot exteriors with all compact surfaces of positive genus essentially embedded |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2508.17504 |