On almost free torus actions and Horrocks conjecture

Details On almost free torus actions and Horrocks conjecture On almost free torus actions and Horrocks conjecture

2012-03-16

arxiv.org/abs/1203.3685v1

Mathematics

Algebraic Topology

8 pages

Scientific paper

We construct a model for cohomology of a space $X$ with torus action. 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. In particular we give a proof of toral rank conjecture in the case of torus dimension $\le5$.

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