C₂ equivariant characteristic classes over the rational Burnside ring

2021/04/24 by Nick Georgakopoulos, Georgakopoulos, Nick
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2104.11945

Abstract

We give minimal presentations for the RO(C₂)-graded Bredon cohomology of the equivariant classifying spaces B_C2U(n), B_C2SO(n) and B_C2Sp(n) with coefficients in the rational Burnside Green functor A_{\mathbf Q}. This results in an efficient description of rational C₂ equivariant Chern, Pontryagin and symplectic characteristic classes. These classes are then related to each other using the inclusions of maximal tori.

Citations

• Equivariant Eilenberg-Mac Lane spectra in cyclic p-groups

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