Geodesic
The Integral Cohomology of Toric Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2006_252_a6,
     author = {M. Franz},
     title = {The {Integral} {Cohomology} of {Toric} {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {61--70},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a6/}
}
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M. Franz. The Integral Cohomology of Toric Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 61-70. http://geodesic.mathdoc.fr/item/TM_2006_252_a6/