Course Archives Theoretical Statistics and Mathematics Unit

Course: Topology II Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus: 1. 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. 2. Categories and functors. Singular homology groups, axiomatic properties, Mayer-Vietoris sequence, homology with coefficients, statement of universal coefficient theorem for homology, simple computation of homolgy groups. 3. 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. Suggested Texts : 1. A. Hatcher, Algebraic Topology, Cambridge University Press (2002). 2. W. S. Massey, A Basic Course in Algebraic Topology, GTM (127), Springer (Indian reprint 2007). 3. J. R. Munkres, Elements of algebraic topology, Addison-Wesley (1984). 4. M. J. Greenberg and J.R. Harper, Algebraic topology: A First Course, Benjamin/ Cummings (1981). 5. I. M. Singer and J. A. Thorpe, Lecture Notes on Elementary Topology and Geometry, UTM, Springer (Indian reprint 2004). 6. E. Spanier, Algebraic Topology, Springer- Verlag (1982). Evaluation: Midterm Exam 30 marks Assignment 20 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 04.pdf 07.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf 18.pdf 20.pdf Solution 09.pdf 12.pdf 14.pdf Semestral 04.pdf 06.pdf 10.pdf 12.pdf 16.pdf 18.pdf Supplementary and Back Paper 06.pdf 16.pdf 18.pdf Top of the page

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