Equivariant characteristic forms in the Cartan model and Borel equivariant cohomology

2015/08/31 by Andreas Kübel, Kübel, Andreas, Thom, Andreas
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1508.07847

openalex publication_date 2015/08/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show the compatibility of the differential geometric and the topological construction of equivariant characteristic classes for compact Lie groups. Our analysis motivates a differential geometric construction for equivariant characteristic classes in the non-compact case. This compatibility is generally assumed and used in various cases, but there is only a proof for compact connected Lie groups in the literature, see the work of Raoul Bott and Loring Tu. Our proof applies and generalizes ideas of Johan Dupont and Ezra Getzler.

Citations

• Gerbes on complex reductive Lie groups
• Lecture Notes on Equivariant Cohomology

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