De Rham 2-Cohomology of Real Flag Manifolds

Author(s)

Del Barco, Viviana ^{[1, 2]} ; Barrera San Martin, Luiz Antonio ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil

^[2] UNR, CONICET, Rosario, Santa Fe - Argentina

• Document type: Journal article
• Source: Symmetry Integrability and Geometry-Methods and Applications; v. 15, 2019.
• Web of Science Citations: 0

Abstract

Let 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 g = Lie(G). This paper computes the second de Rham cohomology group of 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(F Theta,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 F-Theta with coefficients in a ring R. (AU)

• FAPESP's process: 17/13725-4 - Locally conformal geometry on flag manifolds
• Grantee: Viviana Jorgelina Del Barco
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/23896-5 - Invariant structures on real flag manifolds
• Grantee: Viviana Jorgelina Del Barco
• Support Opportunities: Scholarships in Brazil - Post-Doctoral