A Casson-Lin type invariant for links

Eric Harper; Nikolai Saveliev

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arXiv · 0907.1070

A Casson-Lin type invariant for links

Eric Harper·Nikolai Saveliev

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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.

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Eric Harper, Nikolai Saveliev. 2009-11-23. A Casson-Lin type invariant for links. https://arxiv.org/abs/0907.1070

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