# Course

Course No:
M660
Credit:
4
Approval:
2014
PG-Core
Syllabus:
• Homotopy Theory: Fundamental groups and its functorial properties, examples, Van-Kampen Theorem, [8 lectures]
• Covering spaces: Covering spaces, Computation of fundamental groups using coverings. The classification of covering spaces. Deck transformations. [8 lectures]
• Simply connected spaces: Simply connected spaces-Universal covering spaces of locally simply connected and pathwise connected spaces. - Universal covering group of connected subgroups of General Linear groups. [16 lectures]
• Homology groups: Affine spaces, simplexes and chains - Homology groups - Properties of Homology groups. - Chain Complexes, Relation Between one dimensional Homotopy and Homology groups. - (As in sections 8 - 12 of Part II of Greenberg and Harper.) [16 lectures]
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