English

A multivariable Casson-Lin type invariant

Geometric Topology 2019-09-23 v2

Abstract

We introduce a multivariable Casson-Lin type invariant for links in S3S^3. This invariant is defined as a signed count of irreducible SU(2)\operatorname{SU}(2) representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable signatures. We also obtain some results concerning deformations of SU(2)\operatorname{SU}(2) representations of link groups.

Keywords

Cite

@article{arxiv.1805.03050,
  title  = {A multivariable Casson-Lin type invariant},
  author = {Léo Bénard and Anthony Conway},
  journal= {arXiv preprint arXiv:1805.03050},
  year   = {2019}
}

Comments

39 pages, 6 figures; v2: The statement of Theorem 1.1 has changed: our invariant is not equal to the multivariable signature but to a sum of multivariable signatures; the proof has been amended accordingly, final version, to appear in Annales de l'institut Fourier

R2 v1 2026-06-23T01:48:29.057Z