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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 252, Pages 61–70 (Mi tm62)  
This article is cited in 35 scientific papers (total in 35 papers)

The Integral Cohomology of Toric Manifolds

M. Franz

University of Konstanz
Full-text PDF (208 kB) Citations (35)
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Abstract: 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.
Received in February 2005
English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 252, Pages 53–62
DOI: https://doi.org/10.1134/S008154380601007X
Bibliographic databases:
UDC: 514.76+515.165
Language: English
Citation: M. Franz, “The Integral Cohomology of Toric Manifolds”, Geometric topology, discrete geometry, and set theory, Collected papers, Trudy Mat. Inst. Steklova, 252, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 61–70; Proc. Steklov Inst. Math., 252 (2006), 53–62
Citation in format AMSBIB
\Bibitem{Fra06}
\by M.~Franz
\paper The Integral Cohomology of Toric Manifolds
\inbook Geometric topology, discrete geometry, and set theory
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 252
\pages 61--70
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm62}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2255969}
\zmath{https://zbmath.org/?q=an:1350.14036}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 252
\pages 53--62
\crossref{https://doi.org/10.1134/S008154380601007X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746070018}
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    • This publication is cited in the following 35 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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