The Benard-Conway invariant of two-component links
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, 2l)-torus links with the help of the Chebyshev polynomials.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.16161
- arXiv:
- arXiv:2408.16161
- Bibcode:
- 2024arXiv240816161L
- Keywords:
-
- Mathematics - Geometric Topology;
- 57K10;
- 57K31
- E-Print:
- 31 pages, 10 figures