### MA 332: Algebraic Topology

#### January, 2020

### Syllabus

**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, PoincarĂ© duality.

#### Suggested books:

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

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

#### Assignments

Assignments will be posted roughly once in two weeks.

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

#### Midterm examination

**Date:**Fri, Feb 21, 2020**Time:**9:30-11:00 a.m.**Venue:**LH-5, Department of Mathematics, IISc

#### Course Details

**Instructor:**Siddhartha Gadgil**E-mail:***siddhartha.gadgil@gmail.com***Office:**N-15, Department of Mathematics, IISc.**Timing:**Monday, Wednesday, Friday 9:00 am to 10:00 am**Venue:**LH-5, Department of Mathematics, IISc