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.
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