Gerbes, simplicial forms and invariants for families of foliated bundles

Details Gerbes, simplicial forms and invariants for families of foliated bundles Gerbes, simplicial forms and invariants for families of foliated bundles

2003-08-08

arxiv.org/abs/math/0308076v3

Commun.Math.Phys. 253 (2004) 253-282

Mathematics

Differential Geometry

28 pages

Scientific paper

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

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