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math.GT2011★ 6 cited
The Kanenobu knots and Khovanov-Rozansky homology
Andrew Lobb
Kanenobu has given infinite families of knots with the same HOMFLY polynomials. We show that these knots also have the same sl(n) and HOMFLY homologies, thus giving the first examp…
math.GT2011
2-strand twisting and knots with identical quantum knot homologies
Andrew Lobb
Given a knot, we ask how its Khovanov and Khovanov-Rozansky homologies change under the operation of introducing twists in a pair of strands. We obtain long exact sequences in homo…