Ma151a Algebraic and Differential Topology

I taught this course in Fall 2022

We followed Hatcher’s Algebraic Topology (Chapter 2 and 3.1) and Bredon’s Geometry and Topology (mainly Chapter IV and V).

Homework assignments:

• Set 1 - Quotient topology, homotopies (review)
• Set 2 - Simplicial Homology: Problems 3, 6 and 8 in Section 2.1 of Hatcher’s book.
• Set 3 - Chain complexes, relative singular homology
• Set 4 - Relative homology: Problems 16, 25 and 27 in Section 2.1 of Hatcher’s book.
• Set 5 - Axioms of homology: Problem 3 in Ch. IV Section 6 of Bredon’s book; Problems 2, 4, and 8 in Section 2.2 of Hatcher’s book.
• Set 6 - Cellular homology: Exercises 2 and 9 in Bredon’s Section 4.10; Exercise 2 in Bredon’s Section 4.12; Exercise 4 in Bredon’s Section 4.13.
• Set 7 - Differential forms and De Rham cohomology
• Set 8 - Universal Coefficient Theorem

Problem sets for collaborative problem-solving sessions:

• Workshop 1: Simplicial Homology
• Workshop 2: Axioms of homology