English

A Casson-Lin type invariant for links

Geometric Topology 2009-11-23 v3

Abstract

We define an integer valued invariant for two-component links in S^3 by counting projective SU(2) representations of the link group having non-trivial second Stiefel-Whitney class. We show that our invariant is, up to sign, the linking number of the link. Our construction generalizes that of X.-S. Lin who defined a similar invariant for knots in S^3; his invariant equals half the knot signature.

Keywords

Cite

@article{arxiv.0907.1070,
  title  = {A Casson-Lin type invariant for links},
  author = {Eric Harper and Nikolai Saveliev},
  journal= {arXiv preprint arXiv:0907.1070},
  year   = {2009}
}

Comments

New set of generators for the braid group in Section 2

R2 v1 2026-06-21T13:22:11.412Z