Floer homology of brieskorn homology spheres

Every Brieskorn homology sphere Σ(p, q, r) is a double cover of the 3-sphere ramified over a Montesinos knot k(p, q, r). We express the Floer homology of Σ(p, q, r) in terms of certain invariants of the knot k(p, q, r), among which are the knot signature and the Jones polynomial. We also define an integer valued invariant of integral homology 3-spheres which agrees with the μ^¯invariant of W. Neumann and L. Siebenmann for Seifert fibered homology spheres, and investigate its behavior with respect.