$C_2$ equivariant characteristic classes over the rational Burnside ring

Abstract

We give minimal presentations for the $RO(C_2)$-graded Bredon cohomology of the equivariant classifying spaces $B_{C_2}U(n),B_{C_2}SO(n)$ and $B_{C_2}Sp(n)$ with coefficients in the rational Burnside Green functor $A_{\mathbf{Q}}$. 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.

Comments are most welcome! 34 pages. Code is available on https://github.com/NickG-Math/Symmetric_Polynomials

References in corpus (2)

• Equivariant local coefficients and the RO(G)-graded cohomology of classifying spaces
• $C_2$-equivariant Homology Operations: Results and Formulas