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arXiv · 1103.1412

2-strand twisting and knots with identical quantum knot homologies

Andrew Lobb
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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 new way to generate arbitrary numbers of knots with isomorphic homologies and finding an infinite number of mutant knot pairs with isomorphic reduced homologies.

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BibTeXRIS

Andrew Lobb. 2011-05-03. 2-strand twisting and knots with identical quantum knot homologies. https://doi.org/10.2140/gt.2014.18.873

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