De Rham 2-Cohomology of Real Flag Manifolds
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 zer...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210244 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | De Rham 2-Cohomology of Real Flag Manifolds / V. del Barco, L.A.B. San Martin // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862702497825554432 |
|---|---|
| author | del Barco, V. San Martín, L.A.B. |
| author_facet | del Barco, V. San Martín, L.A.B. |
| citation_txt | De Rham 2-Cohomology of Real Flag Manifolds / V. del Barco, L.A.B. San Martin // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T21:24:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210244 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:53Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | del Barco, V. San Martín, L.A.B. 2025-12-04T13:11:30Z 2019 De Rham 2-Cohomology of Real Flag Manifolds / V. del Barco, L.A.B. San Martin // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57T15; 14M15 arXiv: 1811.07854 https://nasplib.isofts.kiev.ua/handle/123456789/210244 https://doi.org/10.3842/SIGMA.2019.051 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. 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. The authors express their gratitude to Lonardo Rabelo for careful reading of a previous version of this manuscript and his useful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications De Rham 2-Cohomology of Real Flag Manifolds Article published earlier |
| spellingShingle | De Rham 2-Cohomology of Real Flag Manifolds del Barco, V. San Martín, L.A.B. |
| title | De Rham 2-Cohomology of Real Flag Manifolds |
| title_full | De Rham 2-Cohomology of Real Flag Manifolds |
| title_fullStr | De Rham 2-Cohomology of Real Flag Manifolds |
| title_full_unstemmed | De Rham 2-Cohomology of Real Flag Manifolds |
| title_short | De Rham 2-Cohomology of Real Flag Manifolds |
| title_sort | de rham 2-cohomology of real flag manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210244 |
| work_keys_str_mv | AT delbarcov derham2cohomologyofrealflagmanifolds AT sanmartinlab derham2cohomologyofrealflagmanifolds |