1. Manifolds in RN, submanifolds,
smooth maps of manifolds, derivatives and tangents, Inverse function
theorem and
immersions, submersions, Transversality, Homotopy and stability, Sards
theorem and Morse functions, embedding manifolds in Euclidean space.
2. Differential Forms and Integration
of forms, Stokes Theorem, Definition of de RhamCohomology.
Suggested Texts :
1. V. Guillemin and A. Pollack, Differential Topology, Prentice-Hall (1974).
2. J.W. Milnor, Topology from the Differentiable Viewpoint, Princeton Univ. Press (1997).
3. J.W. Milnor, Topology from the Differentiable Viewpoint, Univ Press of Virginia
(1965).
- Teacher: Aniruddha C Naolekar