2–strand twisting and knots with identical quantum knot homologies

Lobb, Andrew

doi:10.2140/gt.2014.18.873

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

Andrew Lobb

Geometry & Topology 18 (2014) 873–895

DOI: 10.2140/gt.2014.18.873

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

Volume 18, issue 2 (2014)