INTEGRAL HOMOLOGY OF REAL ISOTROPIC AND ODD ORTHOGONAL GRASSMANNIANS

Lambert, Jordan; Rabelo, Lonardo

doi:https://doi.org/10.18910/89332

INTEGRAL HOMOLOGY OF REAL ISOTROPIC AND ODD ORTHOGONAL GRASSMANNIANS

Lambert, Jordan; Rabelo, Lonardo

Osaka Journal of Mathematics, 2022, 59(4), 853-880

アクセス数:81件（2025-07-16 11:28 集計）

固定URL: https://doi.org/10.18910/89332

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タイトル	INTEGRAL HOMOLOGY OF REAL ISOTROPIC AND ODD ORTHOGONAL GRASSMANNIANS
著者	著者名 Lambert, Jordan
著者	著者名 Rabelo, Lonardo
抄録	We obtain a combinatorial expression for the boundary map coefficients of real isotropic and odd orthogonal Grassmannians. It provides a natural generalization of the known formulas for Lagrangian and maximal isotropic Grassmannians. The results derive from the classification of Schubert cells into four types of covering pairs when identified with signed k-Grassmannian permutations. Our formulas show that the coefficients depend on the changed positions for each permutation pair type. We apply this to obtain an orientability criterion and compute the first and second homology groups for these Grassmannians. Furthermore, we exhibit an apparent symmetry of the boundary map coefficients.
出版者	Osaka University and Osaka Metropolitan University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(4)
ページ	853-880
刊行年月	2022-10
言語	英語
ハンドルURL	https://hdl.handle.net/11094/89332
DOI	https://doi.org/10.18910/89332
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 59, Number 4 （2022-10）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2022, 59(4), p. 853-880
DC.title	INTEGRAL HOMOLOGY OF REAL ISOTROPIC AND ODD ORTHOGONAL GRASSMANNIANS
DC.creator	Lambert, Jordan
DC.creator	Rabelo, Lonardo
DC.publisher	Osaka University and Osaka Metropolitan University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2022-10
DCTERMS.abstract	We obtain a combinatorial expression for the boundary map coefficients of real isotropic and odd orthogonal Grassmannians. It provides a natural generalization of the known formulas for Lagrangian and maximal isotropic Grassmannians. The results derive from the classification of Schubert cells into four types of covering pairs when identified with signed k-Grassmannian permutations. Our formulas show that the coefficients depend on the changed positions for each permutation pair type. We apply this to obtain an orientability criterion and compute the first and second homology groups for these Grassmannians. Furthermore, we exhibit an apparent symmetry of the boundary map coefficients.
DC.identifier	10.18910/89332
DC.format	89332
citation_title	INTEGRAL HOMOLOGY OF REAL ISOTROPIC AND ODD ORTHOGONAL GRASSMANNIANS
citation_author	Lambert, Jordan
citation_author	Rabelo, Lonardo
citation_publisher	Osaka University and Osaka Metropolitan University, Departments of Mathematics
citation_language	英語
citation_date	2022-10
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	4
citation_firstpage	853
citation_lastpage	880
citation_public_url	https://hdl.handle.net/11094/89332
citation_doi_detail	10.18910/89332
citation_doi	https://doi.org/10.18910/89332

INTEGRAL HOMOLOGY OF REAL ISOTROPIC AND ODD ORTHOGONAL GRASSMANNIANS

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