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Geometry and topology of Riemannian foliations via deformations

Grant number: 18/14980-0
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): September 01, 2018
Effective date (End): December 18, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Marcos Martins Alexandrino da Silva
Grantee:Francisco Carlos Caramello Junior
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis, AP.TEM


We intend to extend the applications and techniques on regular Riemannian and Killing foliations, predominant in the works of Prof. Dr. Dirk Töben, and seek generalizations of those results for the case of singular Riemannian foliations. More specifically, we want to cover the following topics: elaboration of a survey on transverse geometry and topology of Riemannian foliations covering the developments in the field that are relevant to this project, invariance of the equivariant basic cohomology and other transverse invariants under deformations and applications to the localization of basic characteristic classes, generalizations of results on regular Riemannian foliations to singular ones using desingularization techniques. We also intend, through the development of the aforementioned topics, to obtain a methodology for approaching other related topics in this theme, such as the geometric finiteness of classifying spaces of Riemannian foliations and the construction of examples of such foliations via inversion of Molino's construction. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ALEXANDRINO, MARCOS M.; CARAMELLO JR, FRANCISCO C.. Leaf closures of Riemannian foliations: A survey on topological and geometric aspects of Killing foliations. EXPOSITIONES MATHEMATICAE, v. 40, n. 2, p. 54-pg., . (18/14980-0, 16/23746-6)
CARAMELLO JR, FRANCISCO C.; TOBEN, DIRK. Equivariant basic cohomology under deformations. MATHEMATISCHE ZEITSCHRIFT, v. 299, n. 3-4, p. 2461-2482, . (18/14980-0)

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