Conway mutation and knot Floer homology
Conway mutation and knot Floer homology
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Peter Lambert-Cole , Indiana University
Mutant knots are notoriously hard to distinguish. Many, butÌýnot all, knot invariants take the same value on mutant pairs. KhovanovÌýhomology with coefficients in Z/2Z is known to beÌýmutation-invariant, while the bigraded knot Floer homology groups canÌýdistinguish mutants such as the famous Kinoshita-Terasaka and ConwayÌýpair. However, Baldwin and Levine conjectured that delta-graded knotÌýFloer homology, a singly-graded reduction of the full invariant, isÌýpreserved by mutation. In this talk, I will give a new proof thatÌýKhovanov homology mod 2 is mutation-invariant. The same strategy canÌýbe applied to delta-graded knot Floer homology and proves theÌýBaldwin-Levine conjecture for mutations on a large class of tangles.