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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 051, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.051
(Mi sigma1487)
 

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
Full-text PDF (515 kB) Citations (1)
References:
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.
Funding agency Grant number
Fundação de Amparo à Pesquisa do Estado de São Paulo 2015/23896-5
2017/13725-4
2012/18780-0
National Council for Scientific and Technological Development (CNPq) 476024/2012-9
V. del Barco supported by FAPESP grants 2015/23896-5 and 2017/13725-4. L.A.B. San Martin supported by CNPq grant 476024/2012-9 and FAPESP grant 2012/18780-0.
Received: January 8, 2019; in final form June 25, 2019; Published online July 5, 2019
Bibliographic databases:
Document Type: Article
MSC: 57T15, 14M15
Language: English
Citation: Viviana del Barco, Luiz Antonio Barrera San Martin, “De Rham 2-Cohomology of Real Flag Manifolds”, SIGMA, 15 (2019), 051, 23 pp.
Citation in format AMSBIB
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\by Viviana~del Barco, Luiz Antonio Barrera~San Martin
\paper De Rham 2-Cohomology of Real Flag Manifolds
\jour SIGMA
\yr 2019
\vol 15
\papernumber 051
\totalpages 23
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\crossref{https://doi.org/10.3842/SIGMA.2019.051}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074521382}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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