Integrated MSc-PhD Program

SYLLABUS

KSM4E05: Differential Geometry

Topics covered: Vector bundles, local and global sections of vector bundles, bundle homomorphisms, subbundles, cotangent bundle, the differential of a function, multilinear algebra, symmetric and alternating tensors, tensors and tensor fields on manifolds, differential forms, the algebra of alternating tensors, differential forms on manifolds, orientations of manifolds, integration on manifolds, integration of differential forms, Stokes’s theorem, de Rham cohomology, the Mayer–Vietoris theorem, the de Rham theorem, singular cohomology, smooth singular homology, the de Rham theorem.

Suggested texts:

1. 1. 1. 1. 1. 1. Introduction to Smooth Manifolds by John M. Lee
               2. Foundations of Differentiable Manifolds and Lie Groups by Frank W. Warner