Expanding Thurston maps and 3-manifolds

• Grant number: 21/12960-5
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: April 01, 2022
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: André Salles de Carvalho
• Grantee: Rodolfo Cesar Macedo Soares
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

This project proposes to study the relationship between complex dynamics and 3-manifolds. A recent construction due to Carvalho-Meyer associates to an expanding Thurston map of the 2-sphere a singular 3-manifold with additional structures such as a pair of singular foliations and a singular-Euclidean metric. The project proposes to describe the topological characteristics of the 3-manifolds obtained and to study the possibility of introducing homogeneous metrics in them. (AU)