| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Fed Juiz de Fora, Dept Matemat, Rua Jose Lourenco Kelmer S-N, Campus Univ, BR-36036900 Juiz De Fora, MG - Brazil
[2] Imecc Unicamp, Dept Matemat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | INDAGATIONES MATHEMATICAE-NEW SERIES; v. 30, n. 5, p. 745-772, SEP 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
Let F-Theta = G/P-Theta be a generalized flag manifold, where G is a real non-compact semi-simple Lie group and P-Theta a parabolic subgroup. A classical result says the Schubert cells, which are the closure of the Bruhat cells, endow F-Theta with a cellular CW structure. In this paper we exhibit explicit parametrizations of the Schubert cells by closed balls (cubes) in R-n and use them to compute the boundary operator partial derivative for the cellular homology. We recover the result obtained by Kocherlakota {[}1995], in the setting of Morse Homology, that the coefficients of partial derivative are 0 or +/- 2 (so that Z(2)-homology is freely generated by the cells). In particular, the formula given here is more refined in the sense that the ambiguity of signals in the Morse-Witten complex is solved. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 08/04628-6 - Geometry of Homogeneous Spaces and Fiber Bundles |
| Grantee: | Lonardo Rabelo |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 07/06896-5 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Luiz Antonio Barrera San Martin |
| Support Opportunities: | Research Projects - Thematic Grants |