JournalsrmiVol. 36, No. 2pp. 485–536

The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics

  • Roberto Rubio

    Weizmann Institute of Science, Rehovot, Israel and Universitat Autònoma de Barcelona, Spain
  • Carl Tipler

    Université de Bretagne Occidentale, Brest, France
The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics cover

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Abstract

We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modeled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of this Lie group on the space of generalized metrics. As an application, we show that the moduli space of generalized metrics is stratified by ILH submanifolds and relate it to the moduli space of usual metrics. Finally, we extend these results to odd exact Courant algebroids.

Cite this article

Roberto Rubio, Carl Tipler, The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics. Rev. Mat. Iberoam. 36 (2020), no. 2, pp. 485–536

DOI 10.4171/RMI/1137