On almost free torus actions and Horrocks conjecture

Yury Ustinovsky

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arXiv · 1203.3685

On almost free torus actions and Horrocks conjecture

Yury Ustinovsky

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Abstract

We construct a model for cohomology of a space $X$ equipped with a torus $T$ action, whose homotopy orbit space $X_{T}$ is formal. This model represents Koszul complex of its equivariant cohomology. Studying homological properties of modules over polynomial ring we derive new bounds on homological rank (dimension of cohomology ring) of $X$ equipped with almost free torus action. We give a proof of toral rank conjecture for spaces with formal quotient in the case of torus dimension $\le5$.

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Yury Ustinovsky. 2012-03-16. On almost free torus actions and Horrocks conjecture. https://arxiv.org/abs/1203.3685

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