This class is a continuation of the study of the Manifolds began in Math 6457. Main topics covered include differential forms, Stokes Theorem, de Rham cohomology, singular homology, and, as time permits, some topics from Riemannian geometry such as the classification theorem for spaces of constant curvature.
Familiarity with manifolds and their tangent spaces (e.g., Math 6457).
Introduction to Smooth Manifolds by John M. Lee, Riemannian Geometry by M. do Carmo, and Algebraic Topology by Allen Hatcher.
The grade is based on class participation (the students are expected to attend all lectures), and homework assignments.