Simplicial homotopy theory

• Grant number: 17/21422-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2017
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ivan Struchiner
• Grantee: Antônio Fittipaldi
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The purpose of this project is to familiarize the student with simplicial homotopy theory. At first, the student will be exposed the that basic definitions and constructions of the theory, including simplicial sets, geometric realization, simplicial homotopy groups, etc. Then, the student will concentrate on the concepts that will lead to the main results of the project: the relation between the homotopy theory of simplicial sets and that of topological spaces. (AU)