### MA 332: Algebraic Topology

#### January 2024

This is the second course in the Algebraic Topology series, following MA 232: Introduction to Algebraic Topology which I taught this academic year. A reasonable background in algebra is also a prerequisite, including at least the structure theorem for (finit ely generated) abelian groups.

#### 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 2-3 weeks. Instead of submitting assignments, students will be asked to solve the problems in lecture, typically the lecture after the due date.

- $H_0$ and reduced homology due by Monday, Feb 5, 2024.

#### Course Details

**Instructor:**Siddhartha Gadgil**E-mail:***siddhartha.gadgil@gmail.com***Office:**N-15, Department of Mathematics, IISc.**Timing:**Tuesday, Thursday 8:30 - 10:00 am.**Venue:**LH-3, Department of Mathematics, IISc.**First meeting:**Tuesday, January 2, 2024.

##### Midterm Examination

**Date:**Thursday, February 22, 2024.**Time:**8:30 - 10:00 am.**Venue:**LH-3, Department of Mathematics, IISc.

The syllabus for the midterm examination is the material covered in lectures up to Thursday, February 15, 2024.

#### Microsoft Teams details

A Team for this course (within IISc) named Algebraic Topology 2024 has been created. Anyone from IISc can also join using the Team code `znr3hi8`

.

There are Teams apps available for Windows, Linux (Debian/Ubuntu and Redhat), Mac, Android and iOS. I would encourage using the Teams chat to ask questions whenever needed.