##### Department of Mathematics,

University of California San Diego

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### Food For Thought

## Itai Maimon

#### UCSD

## An Introduction to Vector Bundles and Characteristic Classes

##### Abstract:

A smooth manifold is a topological structure that admits some standard calculus constructions. A vector bundle over a manifold is a smooth choice of a vector space at every point of the manifold. One motivation for such an object is that the differential of a map between two manifolds is a map between their tangent bundles. At first glance, vector bundles seem as though they should be Cartesian products of the manifold with a vector space. In general, this is false, and certain ``characteristic classes'' are the explicit obstructions. In this talk, we will construct these classes and discuss some theorems explaining why they are of interest to many mathematicians.

### March 13, 2020

### 1:00 PM

### AP&M 5402

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