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International Mathematics Research Notices (2000) 2000:699-708, doi:10.1155/S1073792800000386
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

A fiber integration formula for the smooth Deligne cohomology

Kiyonori Gomi and Yuji Terashima

As is well known, an important operation exists in de Rham cohomology called integration along the fiber for a fiber bundle. In this paper, we extend it to the smooth Deligne cohomology, which is a refinement of ordinary cohomology. First we construct such an explicit map on the Cech cochains and prove a Stokes-type formula which shows that it is a chain map when the fiber has no boundary. Second we prove that the induced map on the smooth Deligne cohomology is canonical; that is, it is independent of all choices used in the construction.


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