Products of real equivariant weight filtrations

TL;DR

This paper establishes a weight filtration on the equivariant cohomology of real algebraic varieties with finite group actions, demonstrating its compatibility with algebraic operations and spectral sequences.

Contribution

It introduces a new weight filtration on equivariant cohomology and proves its compatibility with key algebraic structures and spectral sequences.

Findings

Existence of a weight filtration on equivariant cohomology.

Compatibility with K{"u}nneth isomorphism, cup, and cap products.

Derivation of classical formulas for equivariant cup and cap products.

Abstract

We first show the existence of a weight filtration on the equivariant cohomology of real algebraic varieties equipped with the action of a finite group, by applying group cohomology to the dual geometric filtration. We then prove the compatibility of the equivariant weight filtrations and spectral sequences with K{\"u}nneth isomorphism, cup and cap products, from the filtered chain level. We finally induce the usual formulae for the equivariant cup and cap products from their analogs on the non-equivariant weight spectral sequences.