Title: Geometry and Topology I

Description: The basics of smooth manifolds and smooth maps. Immersions and submersions. Sard's theorem, transversality, and applications. Elements of algebraic topology: homotopy and homotopy equivalence, fundamental group, higher homotopy groups, CW complexes. Calculations of the fundamental group by various techniques, applications. Topological classification of 1- and 2-manifolds. Covering spaces, lifting theorems, classification of coverings, deck transformations. Introduction to fiber bundles and fibrations, homotopy exact sequence of a fibration.

Prerequisite: Prerequisite, Masters students permission of instructor

Credits: 3, S/U grading

Graduate Bulletin Course Information

Course Webpages: