$C_2$ equivariant characteristic classes over the rational Burnside ring

arXiv2104.11945MaRDI QIDQ6366019

Publication date: 24 April 2021

Abstract: We give minimal presentations for the

R O (C_{2})

-graded Bredon cohomology of the equivariant classifying spaces

B_{C_{2}} U (n), B_{C_{2}} S O (n)

and

B_{C_{2}} S p (n)

with coefficients in the rational Burnside Green functor

A_{m a t h b f Q}

. This results in an efficient description of rational

C_{2}

equivariant Chern, Pontryagin and symplectic characteristic classes. These classes are then related to each other using the inclusions of maximal tori.

Mathematics Subject Classification ID

Equivariant homology and cohomology in algebraic topology (55N91) Equivariant homotopy theory in algebraic topology (55P91)

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