Thom polynomials. A primer

TL;DR

This paper provides an accessible overview of Thom polynomials, explaining their role in expressing singularity loci in terms of invariants through examples, aimed at readers new to the topic.

Contribution

It offers a primer on Thom polynomials, illustrating key concepts and examples to facilitate understanding of their applications in singularity theory.

Findings

Thom polynomials relate singularity loci to invariants.

Examples demonstrate how to compute Thom polynomials.

The survey clarifies the conceptual framework for Thom polynomials.

Abstract

The Thom polynomial of a singularity $\eta$ expresses the cohomology class of the $\eta$-singularity locus of a map in terms of the map's simple invariants. In this informal survey -- based on two lectures given at the Isaac Newton Institute in 2024 -- we explore various Thom polynomial concepts with examples.