Algebraic Topology

Department of Mathematics, Indian Institute of Science, Aug-Dec 2016.

Ma 232: Introduction to Algebraic Topology

Timings and Venue:

Venue: LH-V (top floor), Department of Mathematics.

Lecture times: Mon, Wed, Fri: 9:00 - 10:00 a.m.

Instructor and Tutor

Instructor: Siddhartha Gadgil

e-mail: siddhartha DOT gadgil At gmail DOT com

Tutor: Arpan Kabiraj


The fundamental group: Homotopy of maps, multiplication of paths, the fundamental group, induced homomorphisms, the fundamental group of the circle, covering spaces, lifting theorems, the universal covering space, Seifert-Van Kampen theorem, applications.

Simplicial Complexes, Simplicial and Singular homology - Definitions, Properties and Applications.


The main reference for this course is:

  • Hatcher, A., Algebraic Topology, Cambridge Univ. Press, 2002; an Indian Edition is Available and the book is also available online.

Other useful references are the following.

  • Armstong, M.A., Basic Topology, , Springer (India), 2004.

  • Munkres, J. R., Topology, Pearson Education, 2005.
  • Greenberg, M. J., Lectures on Algebraic Topology. W. A. Bejamin Inc., London, 1973.

  • Munkres, J. R., Elements of Algebraic Topology, Addison-Wesley, 1984. Spanier, E. H., Algebraic Topology, tata McGraw-Hill, 1966

Old Course Notes:

A previous version of the course (with related but different content) was taught with a virtual whiteboard (using a Tablet PC). The whiteboards for Fundamental groups and Homology are posted here in PDF format.

Note: The whiteboard files are in Landscape mode. Please ensure that the setting is in this mode when printing and rotate while viewing.