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A
quantum categorification of the Alexander polynomial
Louis-Hadrien Robert and Emmanuel Wagner |
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Geometry & Topology 26 (2022) 1985–2064
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Abstract |
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Using a modified foam evaluation, we give a categorification of the Alexander polynomial of a knot. We also give a purely algebraic version of this knot homology which makes it appear as the infinite page of a spectral sequence starting at the reduced triply graded link homology of Khovanov and Rozansky. |
Keywords
knot homology, Alexander polynomial, foams, Soergel
bimodules
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Mathematical Subject Classification 2010
Primary: 57M27, 57R56
Secondary: 17B10, 17B35, 17B37
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References |
Publication
Received: 15 May 2019
Revised: 10 February 2020
Accepted: 25 February 2021
Published: 12 December 2022
Proposed: Walter Neumann
Seconded: Ciprian Manolescu, Paul Seidel
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Authors |
| Louis-Hadrien Robert | |
| RMATH Université de Luxembourg Esch-sur-Alzette Luxembourg |
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| Emmanuel Wagner | |
| Institut de Mathématiques de Jussieu
- Paris Rive Gauche Université de Paris Sorbonne Université - Campus Pierre et Marie Curie Paris France |
Institut de Mathématiques de
Bourgogne UMR 5584 CNRS Université Bourgogne Dijon France |
