Casson invariant

Summary

The Casson invariant is an integer-valued invariant of oriented integral homology 3-spheres, introduced by Andrew Casson. Informally it counts, with signs, the irreducible representations of the fundamental group into $SU(2)$, up to conjugation, divided by $2$. It reduces modulo $2$ to the Rokhlin invariant, and it has a simple behaviour under Dehn surgery on knots. It was one of the first gauge-theoretic style invariants of $3$-manifolds and led to instanton Floer homology.