Sutured Floer homology and the colored Jones polynomial

joint with J. Elisenda Grigsby

Sutured Floer homology is a new invariant for balanced sutured $3$-manifolds, which was discovered by A. Juh\'asz in the year 2006,  
and which generalizes both Heegaard Floer homology and knot Floer homology.
In a first part of my talk, I will recall the definition of sutured Floer homology and discuss some of its properties.
In a second part, I will demonstrate how sutured Floer homology can be used to  
establish, for every knot $K\subset S^3$ and every integer $n>1$, the existence of a spectral sequence converging from Khovanov's  
categorification of the reduced $n$-colored Jones polynomial to a certain knot Floer homology group, which depends only on the knot $K$ and on the parity of $n$. As a corollary, I will show that Khovanov's categorification of the reduced $n$-colored Jones polynomial detects the unknot for all $n>1$.