Topics on algebraic topology

• Grant number: 17/21378-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2018
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Gabriel Longatto Clemente
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 14/03721-3 - Differential homology and cohomology, gerbes and applications, AP.JP

Abstract

During the first six months, the student will learn about singular homology and cohomology theories, in order to complete his knowledge about basic algebraic topology. Then we will start the study of topological K-theory and we will show explicitly that it is a generalized cohomological theory that obeys all the axioms of Eilenberg-Steenrod, except for the dimension one. (AU)