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Symmetric Products of Equivariantly Formal Spaces

Published online by Cambridge University Press:  20 November 2018

Matthias Franz
Matthias Franz*
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON N6A 5B7 email: mfranz@uwo.ca
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Abstract

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Let $X$ be a $\text{CW}$ 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 $\text{M}$ -varieties are again $\text{M}$ -varieties. This generalizes a result by Biswas and D’Mello about symmetric products of $\text{M}$ -curves. We also discuss several related questions.

Keywords

55N9155S1514P25symmetric productequivariant formalitymaximal varietyGamma product

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 2 , 01 June 2018 , pp. 272 - 281
Copyright
Copyright © Canadian Mathematical Society 2018

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