A quantum categorification of the Alexander polynomial

Emmanuel Wagner; Louis-Hadrien Robert

A quantum categorification of the Alexander polynomial

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arxiv 1902.05648 v3 pith:OF2SG2CJ submitted 2019-02-15 math.GT math.QA

Louis-Hadrien Robert , Emmanuel Wagner This is my paper · ORCID

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keywords alexandercategorificationgivehomologyknotpolynomialalgebraicappear

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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--Rozansky.

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State sums for some super quantum link invariants
math.QA 2019-09 conditional novelty 7.0 of 10

A state sum model is given for U_q(gl_{N|M}) quantum link invariants, and a renormalized invariant in the non-semisimple case is shown to agree with normalized colored Jones polynomials at roots of unity.

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