Floer homology of Brieskorn homology spheres: solution to Atiyah's problem

Details Floer homology of Brieskorn homology spheres: solution to Atiyah's problem Floer homology of Brieskorn homology spheres: solution to Atiyah's problem

1997-01-24

arxiv.org/abs/math/9701211v1

Mathematics

Geometric Topology

Scientific paper

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 $\bar\mu$--invariant of W.~Neumann and L.~Siebenmann and the Jones polynomial. Essential progress is made in proving the homology cobordism invariance of our own $\nu$--invariant.

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