Group theoretic perspective on Dehn fillings: Property P conjecture and beyond
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908751195275264 |
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| author | Ito, Tetsuya Motegi, Kimihiko Teragaito, Masakazu |
| author_facet | Ito, Tetsuya Motegi, Kimihiko Teragaito, Masakazu |
| contents | The Property P Conjecture, which was settled by Kronheimer and Mrowka, asserts that every $3$--manifold obtained by non-trivial Dehn surgery on a non-trivial knot is never simply connected. We propose new perspectives in studying Dehn filling from group theoretic point of view, which stem from several variation of the Property P conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03756 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Group theoretic perspective on Dehn fillings: Property P conjecture and beyond Ito, Tetsuya Motegi, Kimihiko Teragaito, Masakazu Geometric Topology Group Theory Primary: 57K10, Secondary: 57K30, 57M05, 57M07, 20F65 The Property P Conjecture, which was settled by Kronheimer and Mrowka, asserts that every $3$--manifold obtained by non-trivial Dehn surgery on a non-trivial knot is never simply connected. We propose new perspectives in studying Dehn filling from group theoretic point of view, which stem from several variation of the Property P conjecture. |
| title | Group theoretic perspective on Dehn fillings: Property P conjecture and beyond |
| topic | Geometric Topology Group Theory Primary: 57K10, Secondary: 57K30, 57M05, 57M07, 20F65 |
| url | https://arxiv.org/abs/2601.03756 |