Course Archives Theoretical Statistics and Mathematics Unit | |||||||||||||||||
Course: Topology II Instructor: Ramesh Sreekantan Room: G25 Level: Postgraduate Time: Currently offered |
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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:
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Midterm
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