Geodesic
The Integral Cohomology of Toric Manifolds
Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 61-70.

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We prove that the integral cohomology of a smooth, not necessarily compact, toric variety $X_\Sigma$ is determined by the Stanley–Reisner ring of $\Sigma$. This follows from a formality result for singular cochains on the Borel construction of $X_\Sigma$. As a onsequence, we show that the cycle map from Chow groups to Borel–Moore homology is split injective. 
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M. Franz. The Integral Cohomology of Toric Manifolds. Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 61-70. http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a6/

[1] Baskakov I.V., Bukhshtaber V.M., Panov T.E., “Algebry kletochnykh kotsepei i deistviya torov”, UMN, 59:3 (2004), 159–160 | MR

[2] Bifet E., De Concini C., Procesi C., “Cohomology of regular embeddings”, Adv. Math., 82 (1990), 1–34 | DOI | MR | Zbl

[3] Bott R., Tu L.W., Differential forms in algebraic topology, Grad. Texts Math., 82, Springer, New York, 1982 | MR | Zbl

[4] Brion M., “Piecewise polynomial functions, convex polytopes and enumerative geometry”, Parameter spaces, Banach Center Publ., 36, ed. P. Pragacz, Inst. Math. Pol. Acad. Sci., Warszawa, 1996, 25–44 | MR | Zbl

[5] Bukhshtaber V.M., Panov T.E., “Deistviya tora i kombinatorika mnogogrannikov”, Tr. MIAN, 225, 1999, 96–131 | MR | Zbl

[6] Buchstaber V.M., Panov T.E., Torus actions and their applications in topology and combinatorics, Univ. Lect. Ser., 24, Amer. Math. Soc., Providence (RI), 2002 | MR | Zbl

[7] Cox D., “The homogeneous coordinate ring of a toric variety”, J. Alg. Geom., 4 (1995), 17–50 | MR | Zbl

[8] Davis M.W., Januszkiewicz T., “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62 (1991), 417–451 | DOI | MR | Zbl

[9] Fischli S., On toric varieties, Ph.D. Thes., Univ. Bern, 1992; http://www.sws.bfh.ch/~fischli/thesis.pdf

[10] Franz M., “Koszul duality and equivariant cohomology for tori”, Intern. Math. Res. Not., 42 (2003), 2255–2303 | DOI | MR | Zbl

[11] Franz M., Maple package Torhom. Version 1.3.0 (2004), http://www-fourier.ujf-grenoble.fr/~franz/maple/torhom.html

[12] Fulton W., Introduction to toric varieties, Ann. Math. Stud., 131, Princeton Univ. Press, Princeton, 1993 | MR | Zbl

[13] Fulton W., Sturmfels B., “Intersection theory on toric varieties”, Topology, 36 (1997), 335–353 | DOI | MR | Zbl

[14] Gugenheim V.K.A.M., May J.P., On the theory and applications of differential torsion products, Mem. AMS, 142, Amer. Math. Soc., Providence (RI), 1974 | MR

[15] Husemoller D.H., Moore J.C., Stasheff J., “Differential homological algebra and homogeneous spaces”, J. Pure and Appl. Algebra, 5 (1974), 113–185 | DOI | MR | Zbl

[16] Jordan A., Homology and cohomology of toric varieties, Ph.D. Thes., Univ. Konstanz, 1997; http://www.inf.uni-konstanz.de/Schriften/preprints-1998.html#057

[17] May J.P., Simplicial objects in algebraic topology, Van Nostrand Math. Stud., 11, Van Nostrand, Princeton (NJ), 1968 | MR

[18] McCleary J., A user's guide to spectral sequences, 2nd ed., Cambridge Univ. Press, Cambridge, 2001 | MR | Zbl

[19] Notbohm D., Ray N., “On Davis–Januszkiewicz homotopy types I; formality and rationalisation”, Alg. and Geom. Topology, 5 (2005), 31–51 | DOI | MR | Zbl

[20] Totaro B., “Chow groups, Chow cohomology, and linear varieties”, J. Alg. Geom. (to appear)