2–strand twisting and knots with identical quantum knot homologies

Lobb, Andrew¹

¹ Department of Mathematical Sciences, Durham University, Science Labs, South Road, Durham DH1 3LE, UK

Geometry & topology, Tome 18 (2014) no. 2, pp. 873-895.

Résumé

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.

Détail

DOI : 10.2140/gt.2014.18.873

Classification : 57M25
Keywords: Khovanov–Rozansky, knots

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