Geometric manifolds and Orbifolds of dimension 3

• Grant number: 14/23398-2
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2015
• End date: April 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Paiva Barreto
• Grantee: Alexandre Paiva Barreto
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this project we want to develop a study about geometric manifolds and orbifolds of dimension 3. That is, manifolds and orbifolds obtained from the quotient of the eight model geometries of Thurston by discrete groups of isometries. Special attention will be given to Sol and hyperbolic classes.In the first part of the project, we are interested in classifying the double coverings and the involutions of Sol and hyperbolic manifolds. With these informations we will discuss the validity of the Borsuk-Ulam problem on this manifolds.In the second part of this project, we intended to develop a computational study about deformations of geometric manifolds and orbifolds. We begin our work by developing an algorithm that allows us to determine voronoi diagrams of finite sets of points in the model geometries and in geometric manifolds and orbifolds. The next step is to enhance this algorithm to determine Dirichlet polyhedra of geometric manifolds and orbifolds. This polyhedrons will allow us to determine various topological invariant of these manifolds and they will allow us to study degeneration phenomena occurring (which are still poorly understood) over deformation processes. (AU)

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)

BARRETO, ALEXANDRE PAIVA. On the collapsing along deformations of hyperbolic cone 3-manifolds. KYOTO JOURNAL OF MATHEMATICS, v. 56, n. 3, p. 539-557, SEP 2016. (14/23398-2)