Abstract
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 homology and further algebraic structure which is then used to derive topological and computational results. Two of our applications include giving a way to generate arbitrary numbers of knots with isomorphic homologies and finding an infinite number of mutant knot pairs with isomorphic reduced homologies.
Citation
Andrew Lobb. "$2$–strand twisting and knots with identical quantum knot homologies." Geom. Topol. 18 (2) 873 - 895, 2014. https://doi.org/10.2140/gt.2014.18.873
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