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# Symmetric products of equivariantly formal spaces

Published:2017-06-21

• Matthias Franz,
Department of Mathematics, University of Western Ontario, London, Ont. N6A 5B7, Canada
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## 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 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
 MSC Classifications: 55N91 - Equivariant homology and cohomology [See also 19L47] 55S15 - Symmetric products, cyclic products 14P25 - Topology of real algebraic varieties

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