English

The $C_2$-equivariant cohomology of complex projective spaces

Algebraic Topology 2022-05-17 v4

Abstract

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of C2C_2, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside ring Mackey functor. This extension of the RO(C2)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.

Keywords

Cite

@article{arxiv.1811.07355,
  title  = {The $C_2$-equivariant cohomology of complex projective spaces},
  author = {Steven R. Costenoble and Thomas Hudson and Sean Tilson},
  journal= {arXiv preprint arXiv:1811.07355},
  year   = {2022}
}

Comments

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