Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Differential Topology Instructor: Suresh Nayak Room: G23 Level: Postgraduate Time: Currently offered |
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Syllabus Past Exams Syllabus: i) 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. ii) Intersection of transverse manifolds, mod 2 intersection theory and winding numbers. Jordan-Brouwer separation theorem. iii) Orientation of manifolds, Oriented intersection number. Lefschetz fixed point theory. Hopf Degree theorem. Suggested Texts : (a) V. Guillemin and A. Pollack, Differential Topology, Prentice-Hall. (b) J. W. Milnor, Topology from the Differentiable Viewpoint, Univ Press of Virginia (1965). (c) R. Bott and L. W. Tu, Differential forms in algebraic topology, GTM (82), Springer Verlag (1982). Evaluation:
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