The Benard-Conway invariant of two-component links
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918406784024576 |
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| author | Liu, Zedan Saveliev, Nikolai |
| author_facet | Liu, Zedan Saveliev, Nikolai |
| contents | The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU(2) representations of the link group with fixed meridional traces. For two-component links with linking number one, the invariant has been shown to equal a symmetrized multivariable link signature. We extend this result to all two-component links with non-zero linking number. A key ingredient in the proof is an explicit calculation of the Benard-Conway invariant for (2, 2n)-torus links with the help of the Chebyshev polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_16161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Benard-Conway invariant of two-component links Liu, Zedan Saveliev, Nikolai Geometric Topology 57K10, 57K31 The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU(2) representations of the link group with fixed meridional traces. For two-component links with linking number one, the invariant has been shown to equal a symmetrized multivariable link signature. We extend this result to all two-component links with non-zero linking number. A key ingredient in the proof is an explicit calculation of the Benard-Conway invariant for (2, 2n)-torus links with the help of the Chebyshev polynomials. |
| title | The Benard-Conway invariant of two-component links |
| topic | Geometric Topology 57K10, 57K31 |
| url | https://arxiv.org/abs/2408.16161 |