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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Equivariant differential cohomology
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by Andreas Kübel and Andreas Thom PDF
Trans. Amer. Math. Soc. 370 (2018), 8237-8283 Request permission

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
  • MR Author ID: 780176
  • ORCID: 0000-0002-7245-2861
  • Email: andreas.thom@tu-dresden.de
  • 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.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 8237-8283
  • MSC (2010): Primary 55N20, 58A12
  • DOI: https://doi.org/10.1090/tran/7315
  • MathSciNet review: 3852464