K-Theory Torsion

TL;DR

This paper explores the torsion components of K-theory on manifolds, highlighting their differences from cohomology and providing explicit examples including products of real projective spaces and a Calabi-Yau manifold.

Contribution

It offers explicit examples of manifolds with K-theory torsion, illustrating differences from cohomology and discussing implications for brane dimensions in physics.

Findings

K-theory torsion differs from cohomology torsion in certain manifolds.

Explicit examples include products of RP^n and a Calabi-Yau manifold.

Discussion of brane dimensions related to K-torsion.

Abstract

The Chern isomorphism determines the free part of the K-groups from ordinary cohomology. Thus to really understand the implications of K-theory for physics one must look at manifolds with K-torsion. Unfortunately there are not many explicit examples, and usually for very symmetric spaces. Cartesian products of RP^n are examples where the order of the torsion part differs between K-theory and ordinary cohomology. The dimension of corresponding branes is also discussed. An example for a Calabi-Yau manifold with K-torsion is given.