2019
del Barco, Viviana; Martin, Luiz Antonio Barrera San
De Rham 2-Cohomology of Real Flag Manifolds Journal Article
Em: SIGMA, vol. 15, 2019.
Resumo | Links | BibTeX | Tags: cellular homology, characteristic classes, de Rham cohomology, Flag Manifolds, Schubert cell
@article{nokey,
title = {De Rham 2-Cohomology of Real Flag Manifolds},
author = {Viviana del Barco and Luiz Antonio Barrera San Martin},
url = {https://www.emis.de/journals/SIGMA/2019/051/},
doi = {https://doi.org/10.3842/SIGMA.2019.051},
year = {2019},
date = {2019-07-05},
journal = {SIGMA},
volume = {15},
abstract = {Let FΘ=G/PΘ be a flag manifold associated to a non-compact real simple Lie group G and the parabolic subgroup PΘ. This is a closed subgroup of G determined by a subset Θ of simple restricted roots of g=Lie(G). This paper computes the second de Rham cohomology group of FΘ. We prove that it is zero in general, with some rare exceptions. When it is non-zero, we give a basis of H2(FΘ,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 FΘ with coefficients in a ring R.},
keywords = {cellular homology, characteristic classes, de Rham cohomology, Flag Manifolds, Schubert cell},
pubstate = {published},
tppubtype = {article}
}
Let FΘ=G/PΘ be a flag manifold associated to a non-compact real simple Lie group G and the parabolic subgroup PΘ. This is a closed subgroup of G determined by a subset Θ of simple restricted roots of g=Lie(G). This paper computes the second de Rham cohomology group of FΘ. We prove that it is zero in general, with some rare exceptions. When it is non-zero, we give a basis of H2(FΘ,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 FΘ with coefficients in a ring R.