Cech cocycles for differential characteristic classes - An infinity-Lie theoretic construction - Mathematics > Algebraic TopologyReportar como inadecuado




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Abstract: What are called secondary characteristic classes in Chern-Weil theory are arefinement of ordinary characteristic classes of principal bundles fromcohomology to differential cohomology. We consider the problem of refining theconstruction of secondary characteristic classes from cohomology sets tococycle spaces; and from Lie groups to higher connected covers of Lie groups bysmooth infinity-groups, i.e., by smooth groupal A-infinity-spaces. Namely, werealize differential characteristic classes as morphisms frominfinity-groupoids of smooth principal infinity-bundles with connections toinfinity-groupoids of higher U1-gerbes with connections. This allows us tostudy the homotopy fibers of the differential characteristic maps thus obtainedand to show how these describe differential obstruction problems. This appliesin particular to the higher twisted differential spin structures called twisteddifferential string structures and twisted differential fivebrane structures.



Autor: Domenico Fiorenza, Urs Schreiber, Jim Stasheff

Fuente: https://arxiv.org/







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