A quantum categorification of the Alexander polynomial (Q2103500)
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scientific article; zbMATH DE number 7632766
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A quantum categorification of the Alexander polynomial |
scientific article; zbMATH DE number 7632766 |
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A quantum categorification of the Alexander polynomial (English)
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14 December 2022
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The paper constructs a categorification of the Alexander polynomial and a spectral sequence from Khovanov-Rozansky triple-graded link homology to this categorification. This partially resolves a conjecture of Dunfield-Gukov-Rasmussen [\textit{N. M. Dunfield} et al., Exp. Math. 15, No. 2, 129--159 (2006; Zbl 1118.57012)]. The construction is essentially a \(\mathfrak{gl}(1|1)\) version of the authors' previous work for categorifying \(\mathfrak{sl}_n\) link polynomials, overcoming technical challenges where needed,
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knot homology
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Alexander polynomial
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foams
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Soergel bimodules
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categorification
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