Symmetric products of equivariantly formal spaces

TL;DR

This paper proves that symmetric products of equivariantly formal spaces retain their formality, extending known results to a broader class of spaces and applications in algebraic geometry.

Contribution

It demonstrates that symmetric and Gamma-products of equivariantly formal spaces are also equivariantly formal, generalizing previous results to new classes of spaces.

Findings

Symmetric products of equivariantly formal spaces are equivariantly formal.

Symmetric products of quasi-projective M-varieties are M-varieties.

Generalizes results about symmetric products of M-curves.

Abstract

Let X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in a field, then so are all symmetric products of X and in fact all its Gamma-products. In particular, symmetric products of quasi-projective M-varieties are again M-varieties. This generalizes a result by Biswas and D'Mello about symmetric products of M-curves. We also discuss several related questions.