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Instructor: Chitrabhanu Chaudhuri (office M-227, email: chitrabhanu [at] niser [dot] ac [dot] in) |
Texts:
- A. Hatcher, Algebraic Topology.
- John M. Lee, Introduction to Topological Manifolds.
- Munkres, Elements of Algebraic Topology.
Course Resources folder will contain lecture notes, problem sets and supplementary material.
Problem Sets: There will be weekly problem sets which you are encouraged to solve collaboratively.
Exams: Midsem - 23rd February 18:00-20:00 (M2).
Grading percentages: Quizzes (2) 30%, Midterm - 30%, Final - 40%.
External resources: I came to know of these excellent sets of lectures from Prof. Pranav Haridas at KSOM.
- Lectures on Algebraic Topology by Siddhart Gadgil at IISC Bangalore in Fall 2020.
- Lectures on Algebraic Topology by Pierre Albin at University of Illinois at Urbana-Champaign in Spring 2018.
Lecture Plan:
- Week 1: Introduction, Quotient Topology.
- Week 2: Homotopy of Maps, Deformation Retraction, Homotopy equivalence, CW complexes.
- Week 3: CW complexes continued, Fundamental group.
- Week 4: Simply connected spaces, Covering maps and homotopy lifting for covers.
- Week 5: Fundamental group of circle and applications, Van Kampen's Theorem.
- Week 6: Computing fundamental groups using Van-Kampen's theorem.
- Week 7: Covering spaces.