#### Volume 18, issue 2 (2014)

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$2$–strand twisting and knots with identical quantum knot homologies

### Andrew Lobb

Geometry & Topology 18 (2014) 873–895
##### 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.

##### Keywords
Khovanov–Rozansky, knots
Primary: 57M25
##### Publication
Revised: 4 May 2011
Accepted: 9 October 2013
Published: 20 March 2014
Proposed: Tom Mrowka
Seconded: Richard Thomas, Peter Teichner
##### Authors
 Andrew Lobb Department of Mathematical Sciences Durham University Science Labs South Road Durham DH1 3LE UK