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January 2012 Čech cocycles for differential characteristic classes: an ∞-Lie theoretic construction
Domenico Fiorenza, Urs Schreiber, Jim Stasheff
Adv. Theor. Math. Phys. 16(1): 149-250 (January 2012).


What are called secondary characteristic classes in Chern–Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and from Lie groups to higher connected covers of Lie groups by smooth $\infty$-groups, i.e., by smooth groupal $A_\infty$- spaces. Namely, we realize differential characteristic classes as morphisms from $\infty$-groupoids of smooth principal $\infty$-bundles with connections to $\infty$-groupoids of higher $U(1)$-gerbes with connections. This allows us to study the homotopy fibres of the differential characteristic maps thus obtained and to show how these describe differential obstruction problems. This applies in particular to the higher twisted differential spin structures called twisted differential string structures and twisted differential fivebrane structures.


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Domenico Fiorenza. Urs Schreiber. Jim Stasheff. "Čech cocycles for differential characteristic classes: an ∞-Lie theoretic construction." Adv. Theor. Math. Phys. 16 (1) 149 - 250, January 2012.


Published: January 2012
First available in Project Euclid: 23 January 2013

zbMATH: 06171205
MathSciNet: MR3019405

Rights: Copyright © 2012 International Press of Boston


Vol.16 • No. 1 • January 2012
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