fiber integration in differential cohomology
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Application to gauge theory
The refinement of the notion of fiber integration in generalized (Eilenberg-Steenrod) cohomology to differential cohomology.
General discussion of fiber integration for Hopkins-Singer coefficients is in (HopkinsSinger, section 4.10) and for integration over circle fibers in (Bunke-Nikolaus-Völkl 13, section 4.5).
In (Bunke-Schick 09) and precursors, existence of fiber integration in differential cohomology over circle fibers was formalized as a separate axiom (Bunke-Schick 09, def. 1.3).
Mike Hopkins, Isadore Singer, section 4.10 in Quadratic Functions in Geometry, Topology, and M-Theory
Ulrich Bunke, Thomas Schick, Uniqueness of smooth extensions of generalized cohomology theories, J. Topol. 3 (2010), no. 1, 110-156 (arXiv:0901.4423)
Ulrich Bunke, Thomas Nikolaus, Michael Völkl, Differential cohomology theories as sheaves of spectra (arXiv:1311.3188)
Revised on April 29, 2014 10:53:58
by Urs Schreiber