Upsilon-like concordance invariants from 𝔰𝔩n knot cohomology

Lewark, Lukas¹ ; Lobb, Andrew²

¹ Mathematisches Institut, Universität Bern, Bern, Switzerland
² Department of Mathematical Sciences, Durham University, Durham, United Kingdom

Geometry & topology, Tome 23 (2019) no. 2, pp. 745-780.

Résumé

We construct smooth concordance invariants of knots $K$ which take the form of piecewise linear maps ${\gimel }_n\left(K\right):\left[0,1\right]\to ℝ$ for $n\ge 2$. These invariants arise from ${\mathfrak{s}\mathfrak{l}}_n$ 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 ${\mathfrak{s}\mathfrak{l}}_n$ knot cohomology which subsumes many known concordance invariants arising from quantum knot cohomologies.

Détail

DOI : 10.2140/gt.2019.23.745

Classification : 57M25
Keywords: Khovanov–Rozansky cohomology, Knot concordance, Knot Floer homology

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