K-theory. An elementary introduction

TL;DR

This survey provides an accessible introduction to K-theory aimed at motivated college students, covering fundamental concepts suitable for mathematicians from various fields.

Contribution

It offers an elementary, approachable overview of K-theory, making advanced topics accessible to beginners and providing a foundation for further study.

Findings

Accessible explanations of K-theory concepts

Bridging gaps for non-specialists in algebraic topology

Guidance to more comprehensive resources

Abstract

This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college students with little background. Therefore, they are accessible to a mathematician of any speciality willing to understand the subject. A much more complete introduction to K-theory may be found in the "Handbook of K-theory", recently edited by Springer.