$C_2$ equivariant characteristic classes over the rational Burnside ring

Nick Georgakopoulos

$C_2$ equivariant characteristic classes over the rational Burnside ring

Algebraic Topology 2021-04-27 v1

Authors: Nick Georgakopoulos

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.

Keywords

chern classes

Cite

@article{arxiv.2104.11945,
  title  = {$C_2$ equivariant characteristic classes over the rational Burnside ring},
  author = {Nick Georgakopoulos},
  journal= {arXiv preprint arXiv:2104.11945},
  year   = {2021}
}

Comments

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

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