Introduction to Algebraic Topology

Timings and Venue:

Venue: LH-III (ground floor), Department of Mathematics.

Lecture times: Wed & Fri, 11:00 a.m - 12:30 p.m.

First Meeting: Wed, August 3, 2011, 11:00 a.m. (in LH-III).

Tutorial/Quiz times: to be announced.

Course Notes:

The course will be 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.

Syllabus:

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.

References:

The main reference for this course is:

Hatcher, A., Algebraic Topology, Cambridge Univ. Press, 2002- an Indian Edition is Available.

Problems will be assigned from Hatcher and it is recommended that students purchase this book.

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

Lectures with Audio (for Homology):

Lecture 1 (homology): (warning: 15 second waiting on title slide); Technical issue for this lecture - recorded without a mocrophone, so perisitent noise of pen writing on tablet.