Gerbes, simplicial forms and invariants for families of foliated bundles

Abstract

The notion of a gerbe with connection is conveniently reformulated in terms of the simplicial deRham complex. In particular the usual Chern-Weil and Chern-Simons theory is well adapted to this framework and rather easily gives rise to `characteristic gerbes' associated to families of bundles and connections. In turn this gives invariants for families of foliated bundles. A special case is the Quillen line bundle associated to families of flat SU(2)-bundles

28 pages

References in corpus (2)

• The universal gerbe, Dixmier-Douady class, and gauge theory
• A Fourier-Mukai transform for real torus bundles

Cited by in corpus (4)

• Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
• Central extensions of gauge transformation groups of higher abelian gerbes
• Differential characters and cohomology of the moduli of flat Connections
• Invariants of families of flat connections using fiber integration of differential characters