The Weil Model and the Cartan Model

Victor W. Guillemin, Shlomo Sternberg and Jochen Brüning
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Victor W. Guillemin: Massachusetts Institute of Technology, Department of Mathematics
Shlomo Sternberg: Harvard University, Department of Mathematics
Jochen Brüning: Humboldt-Universität Berlin, Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät II

Chapter Chapter 4 in Supersymmetry and Equivariant de Rham Theory, 1999, pp 41-52 from Springer

Abstract: Abstract The results of the last chapter suggest that, for any G⋆ module B we take B⊗ W as an algebraic model for the X × E of Chapter 1, and hence H bas (B ⊗ W) as a definition of the equivariant cohomology of B. In fact, one of the purposes of this chapter will be to justify this definition. However the computation of (B ⊗ W)bas is complicated. So we will begin with a theorem of Mathai and Quillen which shows how to find an automorphism of B ⊗ W which simplifies this computation. For technical reasons we will work with W ⊗ B instead of B ⊗ W and replace W by an arbitrary W⋆ module.

Keywords: Exact Sequence; Short Exact Sequence; Equivariant Cohomology; Invariant Element; Weil Algebra (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-3-662-03992-2_4

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