Combinatorial computation of the motivic Poincare series

Abstract

We give the explicit algorithm computing the motivic generalization of the Poincare series of the plane curve singularity introduced by A. Campillo, F. Delgado and S. Gusein-Zade. It is done in terms of the embedded resolution of the curve. The result is a rational function depending of the parameter q, at q=1 it coincides with the Alexander polynomial of the corresponding link. For irreducible curves we relate this invariant to the Heegard-Floer knot homologies constructed by P. Ozsvath and Z. Szabo. Many explicit examples are considered.

43 pages

References in corpus (3)

• Holomorphic disks and link invariants
• On knot Floer homology and cabling II
• Integrals with respect to the Euler characteristic over spaces of functions and the Alexander polynomial

Cited by in corpus (4)

• Superpolynomials for toric knots from evolution induced by cut-and-join operators
• Challenges of beta-deformation
• q,t-Catalan numbers and knot homology
• Seifert cohomology of trees