Homology and cohomology of real flag manifolds

Author(s)

Lonardo Rabelo

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2012-08-20

Examining board members

Luiz Antonio Barrera San Martin; Ketty Abaroa de Rezende; Lucas Conque Seco Ferreira; Claudio Gorodski; Pedro Luiz Queiroz Pergher

• Advisor: Luiz Antonio Barrera San Martin

Abstract

This thesis presents an approach for the study of topology of real flag manifolds. The homology is obtained by the determination of the boundary operator for the cellular homology. This follows from an explicit parametrization of the Schubert cells which gives a cellular structure for these manifolds. For the cohomology ring of a maximal flag manifold, its generators are found as Stiefel-Whitney classes of a line fiber bundle over the flag manifold (AU)

• FAPESP's process: 08/04628-6 - Geometry of Homogeneous Spaces and Fiber Bundles
• Grantee: Lonardo Rabelo
• Support Opportunities: Scholarships in Brazil - Doctorate