Upsilon-like concordance invariants from sl(n) knot cohomology

Lewark, Lukas; Lobb, Andrew

Abstract

We construct smooth concordance invariants of knots K which take the form of piecewise linear maps Çn.K/W Œ0; 1 ! R for n 2. These invariants arise from sln knot cohomology. We verify some properties which are analogous to those of the invariant ‡ (which arises from knot Floer homology), and some which differ. We make some explicit computations and give some topological applications. Further to this, we define a concordance invariant from equivariant sln knot cohomology which subsumes many known concordance invariants arising from quantum knot cohomologies.

Citation

Lewark, L., & Lobb, A. (2019). Upsilon-like concordance invariants from sl(n) knot cohomology. Geometry & Topology, 23(2), 745-780. https://doi.org/10.2140/gt.2019.23.745

• Journal Article Type: Article
• Acceptance Date: May 12, 2018
• Online Publication Date: Apr 30, 2019
• Publication Date: 2019
• Deposit Date: May 31, 2018
• Publicly Available Date: May 7, 2019
• Journal: Geometry and Topology
• Print ISSN: 1465-3060
• Electronic ISSN: 1364-0380
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Issue: 2
• Pages: 745-780
• DOI: https://doi.org/10.2140/gt.2019.23.745
• Public URL: https://durham-repository.worktribe.com/output/1329713