Floer Homology of Brieskorn Homology Spheres
نویسنده
چکیده
Every Brieskorn homology sphere (p; q; r) is a double cover of the 3{sphere ramiied over a Montesinos knot k(p; q; r). We relate Floer homology of (p; q; r) to certain invariants of the knot k(p; q; r), among which are the knot signature and the Jones polynomial. We also deene an integer valued invariant of integral homology 3{spheres which agrees with the {invariant of W. Neu-mann and L. Siebenmann for Seifert bered homology spheres, and investigate its behavior with respect to homology 4{cobordism. Let p; q, and r be pairwise coprime positive integers. A Brieskorn homology 3{ sphere (p; q; r) is the link of the singularity of f ?1 (0), where f : C 3 ! C is a map of the form f(x; y; z) = x p + y q + z r. The complex conjugation in C 3 acts on (p; q; r) turning it into a double branched cover of S 3 branched over a Montesinos knot k(p; q; r).
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