Twisted K-homology,Geometric cycles and T-duality

TL;DR

This paper compares two models of geometric twisted K-homology, establishes their equivalence, introduces a bundle gerbe description, and constructs a T-duality isomorphism relevant to string theory D-branes.

Contribution

It provides an equivalence between different models of geometric twisted K-homology and introduces a new bundle gerbe-based description, along with a T-duality isomorphism.

Findings

Models of geometric twisted K-homology are equivalent.

A new description using bundle gerbes is provided.

T-duality isomorphism for geometric twisted K-homology is constructed.

Abstract

Twisted $K$-homology corresponds to $D$-branes in string theory. In this paper we compare two different models of geometric twisted $K$-homology and get their equivalence. Moreover, we give another description of geometric twisted $K$-homology using bundle gerbes. We establish some properties of geometric twisted $K$-homology. In the last part we construct $T$-duality isomorphism for geometric twisted $K$-homology.