Course No
MA606
Credit
8
Syllabus
Homotopy Theory: Fundamental groups and its functorial properties, examples,Van- Kampen Theorem, Computation of fundamental group of S1.Covering spaces: Covering spaces, Computation of fundamental groups using cover- ings. Theclassication of covering spaces. Deck transformations.Simply connected spaces: Simply connected spaces-Universal covering spaces of locally simplyconnected and pathwise connected spaces. - Universal covering group of connected subgroupsof General Linear groups.Homology groups: Ane spaces, simplexes and chains - Homology groups - Properties ofHomology groups. - Chain Complexes, Relation Between one dimensional Homotopy andHomology groups. Computation of Homology groups Sn, Brouwer's xed point theorem.
Reference Books
- Armstrong, Basic Topology, Springer, 1983
- Greenberg & Harper, Algebraic Topology: A First Course, Addition Wesley, 1984.
- Munkres, Topology, Pearson Education, 2005. 1974