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