# Course

## MA606 - Topology II

Course No:
MA606
Credit:
8
Approval:
2018
PG-Core
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:
1. Armstrong, Basic Topology, Springer, 1983
2. Greenberg & Harper, Algebraic Topology: A First Course, Addition Wesley, 1984.
3. Munkres, Topology, Pearson Education, 2005. 1974