Products of real equivariant weight filtrations

Fabien Priziac (1)

1 I2M - Institut de Mathématiques de Marseille

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 Künneth 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.

Mots clés: real algebraic varieties; group action; equivariant cohomology and homology; weight filtrations; spectral sequences; Künneth isomorphism; cup and cap products.

Domaines: Géométrie algébrique [math.AG]

Fabien Priziac. Products of real equivariant weight filtrations. Manuscripta mathematica, 2020, ⟨10.1007/s00229-020-01178-2⟩. ⟨hal-01574983v2⟩