The knot complement problem for null-homotopic knots
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918191145418752 |
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| author | Daemi, Aliakbar Lidman, Tye |
| author_facet | Daemi, Aliakbar Lidman, Tye |
| contents | We prove that for three-manifolds satisfying a certain algebraic condition on their fundamental group, null-homotopic knots are determined by their complements. This answers a Kirby Problem posed by Boileau for this special case of 3-manifolds. The argument uses techniques in instanton Floer homology and SU(2)-representation varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The knot complement problem for null-homotopic knots Daemi, Aliakbar Lidman, Tye Geometric Topology 57K30, 57K31, 57R58, 57R65 We prove that for three-manifolds satisfying a certain algebraic condition on their fundamental group, null-homotopic knots are determined by their complements. This answers a Kirby Problem posed by Boileau for this special case of 3-manifolds. The argument uses techniques in instanton Floer homology and SU(2)-representation varieties. |
| title | The knot complement problem for null-homotopic knots |
| topic | Geometric Topology 57K30, 57K31, 57R58, 57R65 |
| url | https://arxiv.org/abs/2511.05472 |