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 .
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