Braid group of the torus and the Klein bottle

• Grant number: 12/01740-5
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2012
• End date: July 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daniel Vendrúscolo
• Grantee: Carolina de Miranda e Pereiro
• Supervisor: John Guaschi
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Université de Caen Basse-Normandie, France
• Associated to the scholarship: 10/18930-6 - Braids groups of the torus and the Klein bottle., BP.DR

Abstract

We intend to study the braids groups of the torus, B_n(T), and the Klein bottle, B_n(K), with algebraic and geometric approach. We intend to give an explicit section to the Fadell-Neuwirth's short exact sequence of such groups, to study the embedding of B_n(K) in B_{2n}(T) and the lower central and derived series of such groups, some relations with the mapping class groups. Moreover we intend to discuss if such groups are linear and ordenables. (AU)