The $C_2$-equivariant cohomology of complex projective spaces

Abstract

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside ring Mackey functor. This extension of the $RO(C_2)$-graded theory allows for the definition of Euler classes, which are used as generators of the cohomology of the projective spaces. As an application, we give an equivariant version of Bezout's theorem.

57 pages, this is a major update. The proof of the main result has been simplified. As an application an equivariant version of Bezout's theorem was added

References in corpus (3)

• Z/2-equivariant and R-motivic stable stems
• $RO(C_2)$-graded cohomology of equivariant Grassmannian manifolds
• The $\mathbb{Z}/p$ ordinary cohomology of $B_{G}U(1)$

Cited by in corpus (1)

• An algebraic $C_2$-equivariant Bézout's theorem