Algebraic v. topological K-theory: a friendly match

TL;DR

This paper provides an accessible introduction to algebraic and topological K-theory, emphasizing their differences and similarities, based on lecture notes from courses in Spain and Argentina.

Contribution

It offers a clear comparison between algebraic and topological K-theory, making complex concepts accessible to newcomers.

Findings

Comparison highlights key differences and similarities

Simplified explanations facilitate understanding of K-theory variants

Educational resource for students and researchers

Abstract

These notes evolved from the lecture notes of a minicourse given in Swisk, the Sedano Winter School on K-theory held in Sedano, Spain, during the week January 22--27 of 2007, and from those of a longer course given in the University of Buenos Aires, during the second half of 2006. They intend to be an introduction to $K$-theory, with emphasis in the comparison between its algebraic and topological variants. We have tried to keep as elementary as possible.