FLOER HOMOLOGY OF BRIESKORN HOMOLOGY SPHERES: SOLUTION TO ATIYAH’S PROBLEM

NIKOLAI SAVELIEV

Abstract. In this paper we answer the question posed by M. Atiyah and give an explicit formula for Floer homology of Brieskorn homology spheres in terms of their branching sets over the 3–sphere. We further show how Floer homology is related to other invariants of knots and 3–manifolds, among which are the μ̄–invariant of W. Neumann and L. Siebenmann and the Jones polynomial. Essential progress is made in proving the homology cobordism invariance of our own ν–invariant.