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Hyperbolic bundles: deformations and invariants

Grant number: 14/00582-2
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): August 01, 2014
Effective date (End): February 28, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Acordo de Cooperação: Coordination of Improvement of Higher Education Personnel (CAPES)
Principal Investigator:Carlos Henrique Grossi Ferreira
Grantee:Felipe de Aguilar Franco
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil


A central question in Riemannian geometry is the following: when does a given manifold admit a certain geometric structure? We are particularly interested in the case of a disc bundle over a closed orientable surface equipped with complex hyperbolic structure. Several examples of such bundles were constructed by the advisor and his collaborators. The next natural step is to begin studying the classifying spaces of these complex hyperbolic bundles, i.e., the corresponding Teichmüller spaces. Hence, we intend to search for new discrete invariants of discrete faithful representations of surface groups into the group of holomorphic isometries of the complex hyperbolic plane. Moreover, we will try to develop a new local version of Poincaré's polyhedron theorem that admits parabolic cycles of vertices and, therefore, could be effectively applied to deformations of the mentioned complex hyperbolic structures. (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)
FRANCO, FELIPE A.; GROSSI, CARLOS H.. Special Elliptic Isometries, Relative SU(2,1)-Character Varieties, and Bendings. JOURNAL OF GEOMETRIC ANALYSIS, v. 31, n. 6, p. 5988-6030, . (14/00582-2)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
FRANCO, Felipe de Aguilar. On spaces of special elliptic n-gons. 2018. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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