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 .

Read more about this topic:  Casson Invariant

Famous quotes containing the word count:

    ... idleness is an evil. I don’t think man can maintain his balance or sanity in idleness. Human beings must work to create some coherence. You do it only through work and through love. And you can only count on work.
    Barbara Terwilliger (b. c. 1940)