2–strand twisting and knots with identical quantum knot homologies

Lobb, Andrew

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.
• Public URL: https://durham-repository.worktribe.com/output/1455969