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Symmetric products of equivariantly formal spaces

  • 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 symmetric product, equivariant formality, maximal variety, Gamma product
MSC Classifications: 55N91, 55S15, 14P25 show english descriptions Equivariant homology and cohomology [See also 19L47]
Symmetric products, cyclic products
Topology of real algebraic varieties
55N91 - Equivariant homology and cohomology [See also 19L47]
55S15 - Symmetric products, cyclic products
14P25 - Topology of real algebraic varieties
 

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