Topological K-Theory of Complex Projective Spaces

TL;DR

This paper computes the K-theory of complex projective spaces using exact sequences, Chern character theory, and Bott periodicity, providing a comprehensive understanding of their topological K-theory structure.

Contribution

It offers a detailed calculation of the K-theory for complex projective spaces, integrating key mathematical tools like exact sequences, Chern characters, and Bott periodicity.

Findings

K-theory groups of complex projective spaces are explicitly computed.

The computation leverages the interplay of exact sequences, Chern characters, and Bott periodicity.

Results deepen understanding of topological invariants of complex projective spaces.

Abstract

We compute the K-theory of complex projective spaces. There are three major ingredients: the exact sequence of K-groups, the theory of Chern character and the Bott Periodicity Theorem.