Introduction to the mapping class group of surfaces

• Grant number: 19/19755-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2019
• End date: August 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Natalia Andrea Viana Bedoya
• Grantee: Fernanda Ferrucci Tegon
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this work, we would like to study the basic objects and concepts to prove the following theorem: Dehn-Lickorish Theorem: The mapping class group of a compact orientable surface is generated by Dehn twists. The proof of this theorem follows the ideas of the proof of a Nielsen theorem that states that the mapping class group of the torus is isomorphic to GL(2,Z).