On Stable -Homology of Torus Knots

Abstract

The stable Khovanov– Rozansky homology of torus knots has been conjecturally described as the Koszul homology of an explicit irregular sequence of polynomials. We verify this conjecture using newly available computational data for -homology. Special attention is paid to torsion. In addition, explicit conjectural formulas are given for the -homology of (3, m)-torus knots for all N and m, which are motivated by higher categorified Jones–Wenzl projectors. Structurally similar formulas are proven for Heegard–Floer homology.

2000 AMS Subject Classification::

• 57M25
• 13D02
• 16E45
• 57-04
• 13P99

Keywords::

• Khovanov-Rozansky homology
• Heegard-Floer homology
• torus knot
• Koszul complex

Notes

¹Available at http://www.singular.uni-kl.de.