Differential CharactersProviding a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner. Differential characters form a model of what is nowadays called differential cohomology, which is the mathematical structure behind the higher gauge theories in physics.

What people are saying  Write a review
We haven't found any reviews in the usual places.
Other editions  View all
Common terms and phrases
A G X absolute differential characters bordism bundle gerbe bundle map Chap character h G characteristic class choose cocycle cohomology class commutative diagram compatible construction cov(h covariant derivative cross product curv curvature deﬁned Deﬁnition denote differential forms diﬂerential dim F dimF E G X exp 27ri exp 2m external product fF curv(h ﬁber bundle fiber integration ﬁber integration map ﬁnd ﬁrst fundamental class G Ck G Hk geometric cycle geometric relative cycle group homomorphism h X h Hence holonomy HopkinsSinger identiﬁcation integral periods integration of differential Lemma Let h G line bundle long exact sequence mapping cone mapping cone complex Math obtain parallel transport Proof real lift reﬁned fundamental class relative characters relative differential characters relative differential cohomology ring structure singular cohomology smooth manifold smooth map smooth singular chain smooth space Stokes theorem stratifold homology topologically trivial transfer map uniquely determined yields