Hyperbolic geometry, knot theory and 3-dimensional manifolds

• Grant number: 13/14257-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2013
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Teotonio Sobrinho
• Grantee: Ricardo Costa de Almeida
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project consists of an introduction to hyperbolic geometry and the theory of knots. It is expected that by the end of the project the student is able to understand the statement of Thurston's theorem on the geometrization of a knot complement in dimension 3.For this to be possible the student will develop a program of studies in basic topology, knot theory, and hyperbolic geometry. If time permits, a study will be made regarding the volume conjecture for hyperbolic knots. (AU)