Differential Cohomology: Categories, Characteristic Classes, and Connections

Understand

We give an overview of differential cohomology from a modern, homotopy-theoretic perspective in terms of sheaves on manifolds.

• Although modern techniques are used, we base our discussion in the classical precursors to this modern approach, such as Chern-Weil theory and differential characters, and include the necessary background to increase accessibility.
• Special treatment is given to differential characteristic classes, including a differential lift of the first Pontryagin class.
• Multiple applications, including to configuration spaces, invertible field theories, and conformal immersions, are also discussed.