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Upsilon-like concordance invariants from $\mathfrak{sl}_n$ knot cohomology

Lukas Lewark and Andrew Lobb

Geometry & Topology 23 (2019) 745–780
Abstract

We construct smooth concordance invariants of knots K which take the form of piecewise linear maps n(K): [0,1] for n 2. These invariants arise from sln knot cohomology. We verify some properties which are analogous to those of the invariant ϒ (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.

Keywords
Khovanov–Rozansky cohomology, Knot concordance, Knot Floer homology
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 4 July 2017
Revised: 14 April 2018
Accepted: 12 May 2018
Published: 8 April 2019
Proposed: András I Stipsicz
Seconded: Rob Kirby, Ciprian Manolescu
Authors
Lukas Lewark
Mathematisches Institut
Universität Bern
Bern
Switzerland
http://www.lewark.de/lukas/
Andrew Lobb
Department of Mathematical Sciences
Durham University
Durham
United Kingdom
http://www.maths.dur.ac.uk/users/andrew.lobb/