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This article is cited in 1 scientific paper (total in 1 paper)
De Rham 2-Cohomology of Real Flag Manifolds
Viviana del Barcoab, Luiz Antonio Barrera San Martina a IMECC-UNICAMP, Campinas, Brazil
b UNR-CONICET, Rosario, Argentina
Abstract:
Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a flag manifold associated to a non-compact real simple Lie group $G$ and the parabolic subgroup $P_{\Theta }$. This is a closed subgroup of $G$ determined by a subset $\Theta $ of simple restricted roots of $\mathfrak{g}=\operatorname{Lie}(G)$. This paper computes the second de Rham cohomology group of $\mathbb{F}_\Theta$. We prove that it is zero in general, with some rare exceptions. When it is non-zero, we give a basis of $H^2(\mathbb{F}_\Theta,\mathbb{R})$ through the Weil construction of closed 2-forms as characteristic forms of principal fiber bundles. The starting point is the computation of the second homology group of $\mathbb{F}_{\Theta }$ with coefficients in a ring $R$.
Keywords:
flag manifold, cellular homology, Schubert cell, de Rham cohomology, characteristic classes.
Received: January 8, 2019; in final form June 25, 2019; Published online July 5, 2019
Citation:
Viviana del Barco, Luiz Antonio Barrera San Martin, “De Rham 2-Cohomology of Real Flag Manifolds”, SIGMA, 15 (2019), 051, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1487 https://www.mathnet.ru/eng/sigma/v15/p51
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Abstract page: | 153 | Full-text PDF : | 37 | References: | 18 |
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