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Dal'nevostochnyi Matematicheskii Zhurnal, 2012, Volume 12, Number 1, Pages 98–107
(Mi dvmg232)
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This article is cited in 2 scientific papers (total in 3 papers)
On almost free torus actions and Horrocks conjecture
Yu. M. Ustinovskii M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We consider a model for cohomology groups of a space $X$ with an
action of torus, representing Koszul complex of its equivariant
cohomology. Studying homological properties of modules over polynomial
ring we derive new estimates on homological rank (total dimension of
rational cohomology) of $X$. In particular, we obtain simple proof of
toral rank conjecture in the case of torus dimension $\le 4$.
Key words:
almost free torus actions, equivariant cohomology, Koszul complex,
moment-angle-complex, bigraded Betti numbers.
Received: 17.01.2012
Citation:
Yu. M. Ustinovskii, “On almost free torus actions and Horrocks conjecture”, Dal'nevost. Mat. Zh., 12:1 (2012), 98–107
Linking options:
https://www.mathnet.ru/eng/dvmg232 https://www.mathnet.ru/eng/dvmg/v12/i1/p98
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