The Benard-Conway invariant of two-component links
Geometric Topology
2026-03-25 v2
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.
Cite
@article{arxiv.2408.16161,
title = {The Benard-Conway invariant of two-component links},
author = {Zedan Liu and Nikolai Saveliev},
journal= {arXiv preprint arXiv:2408.16161},
year = {2026}
}
Comments
Added a paragraph relating our work to that of Daemi and Scaduto on irreducible instanton homology of links. 32 pages, 10 figures