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arXiv · 2002.07645

Equivariant formality of the isotropy action on $\mathbb{Z}_2\oplus \mathbb{Z}_2$-symmetric spaces

Manuel Amann·Andreas Kollross
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Abstract

Compact symmetric spaces are probably one of the most prominent class of formal spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational cohomology algebra. As a generalisation, it is even known that their isotropy action is equivariantly formal. In this article we show that $(\mathbb{Z}_2\oplus \mathbb{Z}_2)$-symmetric spaces are equivariantly formal and formal in the sense of Sullivan, in particular. Moreover, we give a short alternative proof of equivariant formality in the case of symmetric spaces with our new approach.

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BibTeXRIS

Manuel Amann, Andreas Kollross. 2020-02-18. Equivariant formality of the isotropy action on $\mathbb{Z}_2\oplus \mathbb{Z}_2$-symmetric spaces. https://arxiv.org/abs/2002.07645

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