This class is an introduction to differential geometry and topology of manifolds. Topics covered include fundamental group, covering spaces, inverse function theorem, Vector fields, Morse-Sard theorem, embeddings and immersions, and degree theory. If time permits, we will also briefly discuss connections in a vector bundle, Riemannian metrics, and curvature, which are some of the topics from the second half of the course.
Prerequisites
Real analysis, and basic topology.
Textbooks
Instructor's notes in addition to excerpts and references to
Algebraic Topology by Allen Hatcher, and Introduction to Smooth Manifolds by John M. Lee.
Grading
The grade is based on class participation (the students are expected to attend all lectures), and homework assignments.