Course Archives Theoretical Statistics and Mathematics Unit | ||||||
Course: Topology III Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: i) CW -complexes, cellular homology, comparison with singular theory, compu tation of homology of projective spaces. ii) Definition of singular cohomology, axiomatic properties, statement of universal coefficient theorem for cohomology. Betti numbers and Euler characterisitic. Cup and cap product, Poincare duality. Cross product and statement of Kunneth theorem. Degree of maps with applications to spheres. iii) Definition of higher homotopy groups, homotopy exact sequence of a pair. Def inition of fibration, examples of fibrations, homotopy exact sequence of a fibra- tion, its application to computation of homotopy groups. Hurewicz homomor phism, The Hurewicz theorem. The Whitehead Theorem. Suggested Texts : (a) A. Hatcher, Algebraic Topology, Cambridge University Press (2002). (b) M. J. Greenberg and J.R. Harper, Algebraic topology: A First Course, Benjamin/Cummings (1981). (c) E. Spanier, Algebraic Topology, Springer-Verlag (1982). (d) J.W. Vick, Homology Theory: an introduction to algebraic topology, Springer(1994). (e) J. R. Munkres, Elements of algebraic topology, Addison-Wesley (1984). (f) G.E. Bredon, Topology and Geometry, Springer (Indian reprint 2005). Evaluation:
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Midterm
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