Casson Invariant - The Casson Invariant As A Count of Representations

The Casson Invariant As A Count of Representations

Informally speaking, the Casson invariant counts the number of conjugacy classes of representations of the fundamental group of a homology 3-sphere M into the group SU(2). This can be made precise as follows.

The representation space of a compact oriented 3-manifold M is defined as where denotes the space of irreducible SU(2) representations of . For a Heegaard splitting of, the Casson invariant equals times the algebraic intersection of with .