On the structure of Thom polynomials of singularities

2007/08/22 by Feher, L. M., Rimanyi, R.
#32S20 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.0708.3068

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.

Related

• Thom polynomials. A primer
• Thom series of contact singularities
• Interpolation characterization of higher Thom polynomials
• Cobordism realizations of Thom polynomials of singularities
• Thom polynomials for singularities of maps