Equivariant Floer groups for binary polyhedral spaces

Invariants for Homology 3-Spheres

“…The Poincare homology sphere 17 (2,3,5) is canonically oriented as the link of complex surface singularity (1.1). This result is due to Kronheimer (unpublished) and can also be found in [19] and [192]. The map 8' vanishes by a dimension count.…”

Instanton Floer homology for connected sums of Poincaré spheres

“…The result follows the same proof of Proposition 4.1 and Lemma 5.1 of [1]. This is also known to Kronheimer.…”

“…We begin with a review of Floer homology and the Fintushel-Stern spectral sequence, then we turn our attention to the Mayer-Vietoris principle for Floer homology. Next we give explicit calculations for the Poincaré homology sphere (with both orientations) of the higher differentials in the spectral sequence by utilizing Austin's approach [1]. At the end, we complete the proof of Theorem 1.…”

“…Let be a finite subgroup of SU (2), and let P be a graph whose vertexes are the elements in R(Y , SU(2)) for Y = S 3 / . Note that R * (Y , SU(2)) describes a graph ( ) isomorphic to the extended Dynkin diagram of an exceptional root system (see [1] §4.2). By identifying any irreducible representation of which factors through U(1) with its dual, we obtain a quotient graph.…”

“…By identifying any irreducible representation of which factors through U(1) with its dual, we obtain a quotient graph. Define an edge joining two vertexes in P if there is a path connecting the two representations defined by R(Y , SU (2)) in the quotient graph without crossing another flat SU (2)-connection (see [1] §2.1 and §4.2).…”