The symplectic Floer homology of composite knots

Abstract

We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in \cite{li} naturally admits an integer graded lifting, and it formulates a filtration and induced spectral sequence. Such a spectral sequence converges to the symplectic homology of knots in \cite{li}. We show that there is another spectral sequence which converges to the $\mathbb{Z}$-graded symplectic Floer homology for composite knots represented by braids.

28pages, AmsLatex, also available at: http://www.math.okstate.edu/~wli/research/publication.html#recent