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Transactions of the American Mathematical Society

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Equivariant differential cohomology


Authors: Andreas Kübel and Andreas Thom
Journal: Trans. Amer. Math. Soc. 370 (2018), 8237-8283
MSC (2010): Primary 55N20, 58A12
DOI: https://doi.org/10.1090/tran/7315
Published electronically: June 20, 2018
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Abstract: The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de facto cocycles, known as differential cohomology. We will discuss the analog in the case of a group action on the manifold: The definition of equivariant characteristic forms in the Cartan model due to Nicole Berline and Michèle Vergne motivates a refinement of equivariant integral cohomology by all Cartan cocycles. In view of this, we will also review previous definitions critically, in particular the one given in work of Kiyonori Gomi.


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Additional Information

Andreas Kübel
Affiliation: MPI for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Email: kuebel@mis.mpg.de

Andreas Thom
Affiliation: Institut für Geometrie, TU Dresden, 01062 Dresden, Germany
Email: andreas.thom@tu-dresden.de

DOI: https://doi.org/10.1090/tran/7315
Received by editor(s): December 8, 2015
Received by editor(s) in revised form: April 4, 2017, and May 17, 2017
Published electronically: June 20, 2018
Additional Notes: The first author wants to thank the International Max Planck Research School Mathematics in the Sciences for financial support. This research was supported by ERC Starting Grant No. 277728 and ERC Consolidator Grant 681207.
Article copyright: © Copyright 2018 American Mathematical Society

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