Geodesic
On almost free torus actions and Horrocks conjecture
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 98-107

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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 $\le 4$. 
@article{DVMG_2012_12_1_a8,
     author = {Yu. M. Ustinovskii},
     title = {On almost free torus actions and {Horrocks} conjecture},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {98--107},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a8/}
}
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Yu. M. Ustinovskii. On almost free torus actions and Horrocks conjecture. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 98-107. http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a8/