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Upsilon-like concordance
invariants from $\mathfrak{sl}_n$ knot cohomology
Lukas Lewark and Andrew Lobb |
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Geometry & Topology 23 (2019) 745–780
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Abstract |
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We construct smooth concordance invariants of knots which take the form of piecewise linear maps for . These invariants arise from 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 knot cohomology which subsumes many known concordance invariants arising from quantum knot cohomologies. |
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Keywords
Khovanov–Rozansky cohomology, Knot concordance, Knot Floer
homology
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Mathematical Subject Classification 2010
Primary: 57M25
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References |
Publication
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
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Authors |
| Lukas Lewark | |
| Mathematisches Institut Universität Bern Bern Switzerland |
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| http://www.lewark.de/lukas/ | |
| Andrew Lobb | |
| Department of Mathematical
Sciences Durham University Durham United Kingdom |
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| http://www.maths.dur.ac.uk/users/andrew.lobb/ | |
