Course Archives Theoretical Statistics and Mathematics Unit | |||||

Course: Topology IV Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus
1. Smooth manifolds, Differential forms on manifolds, Integration on manifolds, Stoke's theorem, computation of cohomology rings of projective spaces, Borsuk- Ulam theorem. 2. Degree, linking number and index of vector fields, The Poincare-Hopf theorem. 3. Definition and examples of principal bundles and fibre bundles, clutching construction, description of classification theorem (without proof). Suggested Texts :
1. R. Bott and L. W. Tu, Differential forms in algebraic topology, GTM (82), Springer-Verlag (1982). 2. Ib H. Madsen and J. Tornehave, From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes, Cambridge Univ Press (1997). 3. F. W.Warner, Foundations of differentiable manifolds and Lie groups, GTM (94), Springer- Verlag (1983). 4. D. Husemoller, Fibre Bundles, Springer-Verlag (1993). 5. N. Steenrod, The Topology of Fibre Bundles, Princeton Univ Press (1999). Top of the page Past Exams | |||||

Midterm
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