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Franz, Matthias
Symmetric products of equivariantly formal spaces
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 some field \(\Bbbk\), 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.

Keywords:symmetric product, equivariant formality, maximal variety, Gamma product
Categories:55N91, 55S15, 14P25

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