Instanton Homology of Seifert Fibred Homology Three Spheres

For an oriented integral homology 3-sphere 2, A. Casson has introduced an integer invariant A(2) that is defined by using the space £%(2) of conjugacy classes of irreducible representations of ^ ( 2 ) into SU(2) (see [1]). This invariant A(2) can be computed from a surgery or Heegard description of 2 and satisfies A(2) = JU(2) (mod 2), where /i(2) is the Kervaire-Milnor-Rochlin invariant of 2. This powerful new invariant was used to settle an outstanding problem in 3-manifold topology; namely, showing that if 2 is a homotopy 3-sphere, then ju(2) = O. C. Taubes [17], utilizing gauge-theoretic considerations, has reinterpreted Casson's invariant in terms of flat connections. Refining this approach, A. Floer [13] has recently defined another invariant of 2 , its 'instanton homology', which takes the form of an abelian group /*(2) with a natural Z8-grading that is an enhancement of A(2) in that