Refined hexagons for differential cohomology

Abstract

Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential cohomology theories fits into a hexagon on the cohomology level. We show that these differential cohomology theories fit into hexagons on the cocycle level, and the hexagons on the cocycle level induce the hexagons on the cohomology level.

13 pages. A rewritten version. Results and exposition are improved. Comments are welcome. Submitted for publication

References in corpus (2)

• Harmonic Cheeger-Simons characters with applications
• Trivializations of differential cocycles