Course Archives Theoretical Statistics and Mathematics Unit

Course: Topology II Instructor: Aniruddha C Naolekar Room: G25 Level: Postgraduate Time: Currently offered

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: Midterm Exam 40 marks Home Work / Assignment --- marks Final Exam 60 marks Total 100 marks Top of the page Past Exams

Midterm 22.pdf 24.pdf Semestral 22.pdf Supplementary and Back Paper 22.pdf 24.pdf Top of the page

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