# Natalia Kolokolnikova : Thom polynomial and its K-theoretic generalization

Global singularity theory originates from problems in obstruction theory. Consider the following question: is there an immersion in a given homotopy class of maps between two smooth compact manifolds M and N? We can reformulate this question as "is the set of points, where a generic smooth map between M and N is not an immersion, empty"? This set is the simplest example of a singularity. Alternatively, we can ask a question whether the cohomology class of this set is 0 or not. Turns out, there is a universal polynomial depending only on the dimensions of M and N and on the type of singularity, that, when evaluated in the corresponding characteristic classes of M and N, computes the cohomology class of a singularity. This polynomial is called the Thom polynomial, and it is the central notion of singularity theory. In my talk I will give an introduction to singularity theory, define the classic Thom polynomial and talk about different approaches to its K-theoretic generalization.

**Category**: Geometry and Topology**Duration**: 01:24:45**Date**: September 2, 2019 at 3:10 PM**Views**: 174-
**Tags:**seminar, Geometry Seminar

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