Course Archives Theoretical Statistics and Mathematics Unit
Course: Differential Topology
Instructor: Suresh Nayak
Room: G23
Level: Postgraduate
Time: Currently offered
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:
Midterm Exam 50 marks
Home Work / Assignment marks
Final Exam 50 marks
Total 100 marks

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Past Exams
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