Course No
M605
Credit
4
Approval
Syllabus
Basics of point-set topology, quotient topology, connectedness, compactness, Urysohn lemma, Urysohn metrization theorem, paracompactness, Partition of Unity.
Topological groups, connected groups, compact groups, Subgroups of General Linear groups.
Fundamental groups and its functorial properties, examples, Van-Kampen Theorem, Brouwer fixed point theorem, Jordan Curve Theorem.
Covering spaces, Computation of fundamental groups using coverings, classification of covering spaces, Deck transformations.
Simply connected spaces, Universal covering group of connected subgroups of General Linear groups.
Reference Books
- Armstrong, Basic Topology, Springer, 1983.
- Munkres, Topology, Pearson Education, 2005.
- Croom. F.H. Basic Concepts of Algebraic Topology UTM series, Springer, 1978.
- Greenberg & Harper, Algebraic Topology: A First Course, Addition Wesley, 1984.
- Massey, Algebraic Topology: an Introduction, Springer, 1977.