Volume 18, issue 2 (2014)

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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
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 3 May 2011
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