Geometric models of twisted differential K-theory I

TL;DR

This paper constructs a geometric model for even twisted differential K-theory using twisted vector bundles with connection, confirming a long-standing hypothesis for torsion class twists.

Contribution

It introduces a new geometric model for even twisted differential K-theory with torsion class twists, satisfying key axioms and confirming a longstanding hypothesis.

Findings

Model satisfies Kahle and Valentino's axioms

Uses twisted vector bundles with connection as cocycles

Confirms twisted vector bundles define twisted differential K-theory

Abstract

This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth U(1)-gerbes with connection, and we use twisted vector bundles with connection as cocycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. This paper confirms a long-standing hypothetical idea that twisted vector bundles with connection define twisted differential K-theory.