Volume 23, issue 2 (2019)

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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

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.

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Khovanov–Rozansky cohomology, Knot concordance, Knot Floer homology
Mathematical Subject Classification 2010
Primary: 57M25
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
Lukas Lewark
Mathematisches Institut
Universität Bern
Andrew Lobb
Department of Mathematical Sciences
Durham University
United Kingdom