Algebraic Topology

Code: MA 643 | L-T-P-C: 4-0-0-8

 

Prerequisites: MA549 Topology or equivalent

Preamble: This course introduces the basic concepts and tools from algebraic topology and provides an important viewpoint for anyone who wishes to pursue further study in the field of geometry and topology.

Syllabus: Homotopy of paths, fundamental group of a space, homomorphism between fundamental groups induced by a map between spaces, homotopy equivalence and homotopy type, the Seifert-van Kampen's theorem and its applications. Covering spaces: Definition and examples, lifting of paths, fundamental group of a covering space, lifting of maps, deck transformations and group actions, regular covering spaces and quotient spaces. Homology: Simplicial homology, singular homology, invariance of homology groups under homotopy, excision, degree of a map from S^n to itself, cellular homology, Mayer-Vietoris sequen ces, homology with co-efficients.

Texts/References:

1. W. S. Massey, A Basic Course in Algebraic Topology, Springer, 1991.
2. A. Hatcher, Algebraic Topology, Cambridge, 2002.
3. J. R. Munkres, Elements of Algebraic Topology, Perseus Publishing, 1984.