A quantum categorification of the Alexander polynomial

Abstract

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.

v2: A technical Proposition was missing, now included as an Appendix. 57 pages, many figures. Comments welcome! v3: Some typos corrected. Introduction re-written

References in corpus (6)

• Floer homology and knot complements
• Functoriality of colored link homologies
• A closed formula for the evaluation of ${\mathfrak{sl}}_N$-foams
• Annular Evaluation and Link Homology
• Remarks on coloured triply graded link invariants
• A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology

Cited by in corpus (3)

• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras
• Symmetries of ${\mathfrak{gl}}_N$-foams