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

Lewark, Lukas; Lobb, Andrew (2019). Upsilon-like concordance invariants from sl(n) knot cohomology. Geometry & Topology, 23(2), pp. 745-780. Mathematical Sciences Publishers 10.2140/gt.2019.23.745

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We construct smooth concordance invariants of knots K which take the form of piecewise linear maps ℷₙ(K):[0,1]→R 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Lewark, Lukas Pascal

Subjects:

500 Science > 510 Mathematics

ISSN:

1465-3060

Publisher:

Mathematical Sciences Publishers

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

17 Feb 2020 15:11

Last Modified:

13 Mar 2021 13:47

Publisher DOI:

10.2140/gt.2019.23.745

ArXiv ID:

1707.00891

BORIS DOI:

10.7892/boris.139951

URI:

https://boris.unibe.ch/id/eprint/139951

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