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A quantum categorification of the Alexander polynomial

Louis-Hadrien Robert and Emmanuel Wagner

Geometry & Topology 26 (2022) 1985–2064

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.

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knot homology, Alexander polynomial, foams, Soergel bimodules
Mathematical Subject Classification 2010
Primary: 57M27, 57R56
Secondary: 17B10, 17B35, 17B37
Received: 15 May 2019
Revised: 10 February 2020
Accepted: 25 February 2021
Published: 12 December 2022
Proposed: Walter Neumann
Seconded: Ciprian Manolescu, Paul Seidel
Louis-Hadrien Robert
Université de Luxembourg
Emmanuel Wagner
Institut de Mathématiques de Jussieu - Paris Rive Gauche
Université de Paris
Sorbonne Université - Campus Pierre et Marie Curie
Institut de Mathématiques de Bourgogne
UMR 5584
Université Bourgogne