Volume 18, issue 1 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
DAHA and plane curve singularities

Ivan Cherednik and Ian Philipp

Algebraic & Geometric Topology 18 (2018) 333–385

We suggest a relatively simple and totally geometric conjectural description of uncolored daha superpolynomials of arbitrary algebraic knots (conjecturally coinciding with the reduced stable Khovanov–Rozansky polynomials) via the flagged Jacobian factors (new objects) of the corresponding unibranch plane curve singularities. This generalizes the Cherednik–Danilenko conjecture on the Betti numbers of Jacobian factors, the Gorsky combinatorial conjectural interpretation of superpolynomials of torus knots and that by Gorsky and Mazin for their constant term. The paper mainly focuses on nontorus algebraic knots. A connection with the conjecture due to Oblomkov, Rasmussen and Shende is possible, but our approach is different. A  motivic version of our conjecture is related to p–adic orbital A–type integrals for anisotropic centralizers.

Hecke algebra, Jones polynomial, HOMFLYPT polynomial, Khovanov-Rozansky homology, algebraic knot, Macdonald polynomial, plane curve singularity, compactified Jacobian, Puiseux expansion, orbital integral
Mathematical Subject Classification 2010
Primary: 14H50, 17B45, 20C08, 20F36, 33D52, 57M25
Secondary: 17B22, 22E50, 22E57, 30F10, 33D80
Supplementary material

Appendices A and B

Received: 28 October 2016
Revised: 15 May 2017
Accepted: 12 June 2017
Published: 10 January 2018
Ivan Cherednik
Mathematics Department
University of North Carolina
Chapel Hill, NC
United States
Ian Philipp
Mathematics Department
University of North Carolina
Chapel Hill, NC
United States