  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.

Geometric Topology