In 1984, Casson constructed an invariant for homology 3-spheres by counting irreducible SU(2) representations, and he applied the invariant to the Hauptvermutung in dimension four. In 1992, X.-S. Lin defined a closely related invariant for knots by counting irreducible SU(2) representations of the knot group with meridional trace zero. Both invariants admit gauge theoretic interpretations leading to the refinements of Floer's instanton homology and to the knot Floer homology.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3651