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

Abstract

We construct smooth concordance invariants of knots which take the form of piecewise linear maps from [0,1] to R, one for each n greater than or equal to 2. These invariants arise from sl(n) knot cohomology. We verify some properties which are analogous to those of the invariant Upsilon (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 sl(n) knot cohomology which subsumes many known concordance invariants arising from quantum knot cohomologies.

25 pages, 5 figures. V2: minor changes and corrections. This version corresponds to the published article

References in corpus (3)

• New Quantum Obstructions to Sliceness
• Notes on the knot concordance invariant Upsilon
• Deformations of colored sl(N) link homologies via foams

Cited by in corpus (5)

• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Linear independence of rationally slice knots
• Braids with as many full twists as strands realize the braid index
• Categorical lifting of the Jones polynomial: a survey
• Transverse link invariants from the deformations of Khovanov ${\mathfrak{sl}}_3$-homology