Poincaré Polynomials and Curvature Operators of Symmetric Spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913993231171584 |
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| author | Petersen, Peter Stanfield, James |
| author_facet | Petersen, Peter Stanfield, James |
| contents | We compute explicit formulas for the curvature operators and Poincaré polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincaré polynomials using quantum numbers, giving a formula that mirrors the known formula for the Euler characteristic. For the curvature operators, we show that their maximum eigenvalue is always bounded above by the Einstein constant, with equality attained precisely by the Hermitian symmetric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poincaré Polynomials and Curvature Operators of Symmetric Spaces Petersen, Peter Stanfield, James Differential Geometry 53C30. 53C35, 57T15 We compute explicit formulas for the curvature operators and Poincaré polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincaré polynomials using quantum numbers, giving a formula that mirrors the known formula for the Euler characteristic. For the curvature operators, we show that their maximum eigenvalue is always bounded above by the Einstein constant, with equality attained precisely by the Hermitian symmetric spaces. |
| title | Poincaré Polynomials and Curvature Operators of Symmetric Spaces |
| topic | Differential Geometry 53C30. 53C35, 57T15 |
| url | https://arxiv.org/abs/2508.11236 |