Real hyperbolic bundles over surfaces

• Grant number: 14/26284-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2015
• End date: September 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Ananin
• Grantee: Christian Vilas Boas Lemos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goal of the project is the construction of new hyperbolic disc bundles over surfaces. We initially plan to present a new and more systematic construction of the known examples; eventually, we expect to improve the results of Feng Luo on the best known bound for the Gromov-Lawson-Thurston conjecture. The project is planned for 2-3 years, but we expect some developments to take place already in the first year. In spite of being young, the student has a considerable mathematical background; for instance, during the entire second semester, he attended to advanced undergraduate and graduate level seminars.