Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Topology II Instructor: Aniruddha C Naolekar Room: G25 Level: Postgraduate Time: Currently offered |
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Syllabus Past Exams Syllabus: i) Review of fundamental groups, necessary introduction to free product of groups, Van Kampens theorem. Covering spaces, lifting properties, Universal cover, classification of covering spaces, Deck transformations, properly discontinuous action, covering manifolds, examples. ii) Categories and functors. Simplicial homology. Singular homology groups, axiomatic properties, Mayer-Vietoris sequence, homology with coefficients, statement of universal coefficient theorem for homology, simple computation of homology groups. iii) CW-complexes and Cellular homology, Simplicial complex and simplicial homology as a special case of Cellular homology, Relationship between fundamental group and first homology group. Computations for projective spaces, surfaces of genus g. Suggested Texts : (a) A. Hatcher, Algebraic Topology, Cambridge University Press (2002). (b) W. S. Massey, A basic course in algebraic topology, GTM (127), Springer (1991). (c) J. R. Munkres, Topology: a first course, Prentice-Hall (1975). (d) J. R. Munkres, Elements of algebraic topology, Addison-Wesley (1984). (e) M. J. Greenberg, Lectures on algebraic topology, Benjamin (1967). (f) I. M. Singer and J. A. Thorpe, Lecture notes on elementary topology and geometry, UTM, Springer. (g) E. Spanier, Algebraic Topology, Springer-Verlag (1982). Evaluation:
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Midterm
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