Singular 3-manifolds via expanding Thurston maps

• Grant number: 25/01655-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: June 23, 2025
• End date: June 22, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: André Salles de Carvalho
• Grantee: Rodolfo Cesar Macedo Soares
• Supervisor: Roesch
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Institut De Mathématiques De Toulouse, France
• Associated to the scholarship: 21/12960-5 - Expanding Thurston maps and 3-manifolds, BP.DD

Abstract

This project explores the relationship between complex dynamics and 3-manifolds. A recent construction due to Carvalho-Hall-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, in some cases, a singular-Euclidean metric. This project proposes to further the study of these 3-dimensional spaces and the relationship between their topology and geometry and dynamical properties of the associated Thurston map. It describes the one year work plan for the student while he is at University Toulouse 3 Paul Sabatier - Institut de Matématiques under the supervision of Prof. Pascale Roesch, an expert in complex dynamics. (AU)