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arXiv · 2408.16161

The Benard-Conway invariant of two-component links

Zedan Liu·Nikolai Saveliev
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Abstract

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.

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Zedan Liu, Nikolai Saveliev. 2024-12-11. The Benard-Conway invariant of two-component links. https://doi.org/10.2140/pjm.2026.341.379

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