MA 332: Algebraic Topology

January, 2020


Homology : Singular homology, excision, Mayer-Vietoris theorem, acyclic models, CW-complexes, simplicial and cellular homology, homology with coefficients.

Cohomology : Comology groups, relative cohomology, cup products, cap product, orientation on manifolds, Poincaré duality.

Suggested books:

We will be following Hacher's book (available online).

  1. Hatcher, A., Algebraic Topology, Cambridge Univ. Press, 2002 (Indian edition is available).
  2. Rotman, J, An Introduction to Algebraic Topology, Graduate Texts in Mathematics, 119, Springer-Verlag, 1988.
  3. Munkres, I. R., Elements of Algebraic Topology, Addison-Wesiley, 1984.


Assignments will be posted roughly once in two weeks.

  1. Homology from definitions due by Monday, Feb 10, 2020.
  2. Proof of Whitehead's theorem due by Thursday, Apr 2, 2020.

Midterm examination

Course Details