Class Notes for Math 872: Algebraic Topology, Instructor Susan Hermiller

Laura Lynch, University of Nebraska - Lincoln

Abstract

The course begins with a review of Math 871 topics, including quotient topology and homotopy fundamental groups and covering spaces). Then builds on these to develop methods to build topological spaces as cell complexes, in order to compute many fundamental groups with the Seifert-Van Kampen Theorem and in order to classify covering spaces (the “Galois correspondence”). The course ends with the basics of homology, including the use of the Mayer-Vietoris Thorem to compute homology groups.