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.