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

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
$2$–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