On elementary invariants of genus one knots and Seifert surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908682354163712 |
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| author | Lescop, Christine |
| author_facet | Lescop, Christine |
| contents | This elementary article introduces easy-to-manage invariants of genus one knots in homology 3-spheres. To prove their invariance, we investigate properties of an invariant of 3-dimensional genus two homology handlebodies called the Alexander form. The Alexander form of a 3-manifold E with boundary contains all Reidemeister torsions of link exteriors obtained by attaching two-handles along the boundary of E. It is a useful tool for studying Alexander polynomials and Reidemeister torsions. We extract invariants of genus one Seifert surfaces from the Alexander form of their exteriors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04707 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On elementary invariants of genus one knots and Seifert surfaces Lescop, Christine Geometric Topology 57K10 (Primary) 57K31, 57K14, 57K16, 57K20 (Secondary) This elementary article introduces easy-to-manage invariants of genus one knots in homology 3-spheres. To prove their invariance, we investigate properties of an invariant of 3-dimensional genus two homology handlebodies called the Alexander form. The Alexander form of a 3-manifold E with boundary contains all Reidemeister torsions of link exteriors obtained by attaching two-handles along the boundary of E. It is a useful tool for studying Alexander polynomials and Reidemeister torsions. We extract invariants of genus one Seifert surfaces from the Alexander form of their exteriors. |
| title | On elementary invariants of genus one knots and Seifert surfaces |
| topic | Geometric Topology 57K10 (Primary) 57K31, 57K14, 57K16, 57K20 (Secondary) |
| url | https://arxiv.org/abs/2304.04707 |