K-Theory, D-Branes and Ramond-Ramond Fields

Understand

This thesis is dedicated to the study of K-theoretical properties of D-branes and Ramond-Ramond fields.

• We construct abelian groups which define a homology theory on the category of CW-complexes, and prove that this homology theory is equivalent to the bordism representation of KO-homology, the dual theory to KO-theory.
• We construct an isomorphism between our geometric representation and the analytic representation of KO-homology, which induces a natural equivalence of homology functors.
• We apply this framework to describe mathematical properties of D-branes in type I String theory.