Course Archives Theoretical Statistics and Mathematics Unit
Course: Topology IV
Level: Postgraduate
Time: Currently not offered
Past Exams


[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 construction, 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)

Top of the page

Past Exams
Supplementary and Back Paper

Top of the page

[ Semester Schedule ][ SMU ] [Indian Statistical Institute]