Braid groups and related structures

• Grant number: 10/52714-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2011
• End date: August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daciberg Lima Gonçalves
• Grantee: Rym Karoui
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project deals about the development of certain ideas on the prospects opened by the work of my thesis. Initially I plan to prolong the results obtained for the 2-sphere to the case of a surface of genus 1 (for example the torus) and then generalize them to a surface of higher genus. My intentions at first are the following: - Try to get a presentation of the torus braid group by applying the techniques of graph presentations of the paper of Vlad Sergiesc for the case of the plane and the paper of P. Bellingeri and V. V. Verchinine for the case of the sphere. Then generalize to surfaces with genus grater than or equal to 1. - Find the nodal relations for the pur braid group on the torus. Get a presentation of the inverse braid monoid of the punctured torus with n-punctures. - Get a presentation of the inverse mapping class monoid of the n-punctured torus. - Get a presentation of the graded Lie algebra associated with the pure mapping class group of the n-punctured torus. (AU)