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Dal'nevost. Mat. Zh., 2012, Volume 12, Number 1, Pages 98–107 (Mi dvmg232)  

This article is cited in 1 scientific paper (total in 2 paper)

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.

Full text: PDF file (237 kB)
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Document Type: Article
UDC: 515.145.23, 515.145.25
MSC: 55R20
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

Citation in format AMSBIB
\Bibitem{Ust12}
\by Yu.~M.~Ustinovskii
\paper On almost free torus actions and Horrocks conjecture
\jour Dal'nevost. Mat. Zh.
\yr 2012
\vol 12
\issue 1
\pages 98--107
\mathnet{http://mi.mathnet.ru/dvmg232}


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    Erratum

    This publication is cited in the following articles:
    1. Yu. M. Ustinovskii, “Pismo v redaktsiyu”, Dalnevost. matem. zhurn., 14:1 (2014), 122–122  mathnet
    2. Yu. M. Ustinovskii, “On models of cohomology rings of spaces with a torus action”, Russian Math. Surveys, 69:4 (2014), 765–767  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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