On the structure of Thom polynomials of singularities
Algebraic Geometry
2007-08-23 v1 Algebraic Topology
Abstract
Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this paper we show that this is a special case of a product rule. The product rule enables us to calculate the Thom polynomials of singularities if we know the Thom polynomial of the product singularity. As a special case of the product rule we define a formal power series (Thom series, Ts_Q) associated with a commutative, complex, finite dimensional local algebra Q, such that the Thom polynomial of {\em every} singularity with local algebra Q can be recovered from Ts_Q.
Keywords
Cite
@article{arxiv.0708.3068,
title = {On the structure of Thom polynomials of singularities},
author = {L. M. Feher and R. Rimanyi},
journal= {arXiv preprint arXiv:0708.3068},
year = {2007}
}