Course Archives Theoretical Statistics and Mathematics Unit
Course: Topology IV
Instructor: Aniruddha Naolekar
Room: G25
Level: Postgraduate
Time: Currently offered
Syllabus
Past Exams


Syllabus:

[Prerequisite: Differential Geometry I] i) Smooth manifolds, differential forms on manifolds, integration on manifolds, Stokes theorem, computation of cohomology rings of projective spaces, Borsuk Ulam theorem. ii) Degree, linking number and index of vector fields, the Poincare-Hopf theorem. iii) Definition and examples of principal bundles and fibre bundles, clutching con- struction, description of classification theorem (without proof).

Suggested Texts :
(a) R. Bott and L. W. Tu, Differential forms in algebraic topology, GTM (82), Springer-Verlag (1982).
(b) Ib H. Madsen and J. Tornehave, From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes, Cambridge Univ Press (1997).
(c) F. W. Warner,t Foundations of differentiable manifolds and Lie groups, GTM (94), Springer-Verlag (1983).
(d) D. Husemoller, Fibre Bundles, Springer-Verlag (1993).
(e) N. Steenrod, The Topology of Fibre Bundles, Princeton Univ Press (1999)

Evaluation:
Midterm Exam 40 marks
Home Work / Assignment marks
Final Exam 60 marks
Total 100 marks

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