2–strand twisting and knots with identical quantum knot homologies

Lobb, Andrew

doi:10.2140/gt.2014.18.873

2–strand twisting and knots with identical quantum knot homologies

Lobb, Andrew

Authors

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

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.

Citation

Lobb, A. (2014). 2–strand twisting and knots with identical quantum knot homologies. Geometry & Topology, 18(2), 873-895. https://doi.org/10.2140/gt.2014.18.873

Journal Article Type	Article
Acceptance Date	Oct 9, 2013
Online Publication Date	Mar 20, 2014
Publication Date	Mar 20, 2014
Deposit Date	Apr 30, 2014
Publicly Available Date	May 13, 2014
Journal	Geometry and Topology
Print ISSN	1465-3060
Electronic ISSN	1364-0380
Publisher	Mathematical Sciences Publishers (MSP)
Peer Reviewed	Peer Reviewed
Volume	18
Issue	2
Pages	873-895
DOI	https://doi.org/10.2140/gt.2014.18.873
Keywords	Khovanov–Rozansky, Knots.

Files

Published Journal Article (396 Kb)
PDF

Copyright Statement
First published in Geometry and Topology in 18 (2014), published by Mathematical Sciences Publishers. © 2014 Mathematical Sciences Publishers. All rights reserved.