EQUIVARIANT KNOT SIGNATURES AND FLOER HOMOLOGIES

Abstract

In this paper, we give a description of the equivariant signature of knots from the symplectic topology point of view. For certain knots K in S3, we define a symplectic Floer homology for the representation space of the knot group π1 (S3\ K) into SU(2) with trace [Formula: see text] along all meridians (p is an odd prime and 0<k<p). The symplectic Floer homology of knots is a new invariant of knots and its Euler number is half of the equivariant signature of knots.