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Topics on algebraic topology

Grant number: 17/21378-2
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): March 01, 2018
Effective date (End): December 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Fabio Ferrari Ruffino
Grantee:Gabriel Longatto Clemente
Home 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)