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

Lewark, Lukas; Lobb, Andrew

doi:10.2140/gt.2019.23.745

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

Lewark, Lukas; Lobb, Andrew

Authors

Lukas Lewark

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

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

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Copyright Statement
First published in Geometry & Topology in Vol. 23 (2019), No. 2, published by Mathematical Sciences Publishers. © 2019 Mathematical Sciences Publishers. All rights reserved.