2017/01/04 by Lambert-Cole, Peter · 1 citation
#57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1701.00880
We give a new, elementary proof that Khovanov homology with ℤ/2ℤ--coefficients is invariant under Conway mutation. This proof also gives a strategy to prove Baldwin and Levine's conjecture that δ--graded knot Floer homology is mutation--invariant. Using the Clifford module structure on \widetildeHFK induced by basepoint maps, we carry out this strategy for mutations on a large class of tangles. Let L' be a link obtained from L by mutating the tangle T. Suppose some rational closure of T corresponding to the mutation is the unlink on any number of components. Then L and L' have isomorphic δ--graded \widehatHFK-groups over ℤ/2ℤ as well as isomorphic Khovanov homology over ℚ. We apply these results to establish mutation--invariance for the infinite families of Kinoshita-Terasaka and Conway knots. Finally, we give sufficient conditions for a general Khovanov-Floer theory to be mutation--invariant.