MA 232: Introduction to algebraic topology
Credits: 3:0
Prerequisite courses: MA 231 and MA 212
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 Homology: Simplicial complexes, chain complexes, definitions of the simplicial homology groups, properties of homology groups, applications.
Suggested books :
- Armstrong, M.A., Basic Topology, Springer (India), 2004.
- Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.
- Kosniowski, C.A., First Course in Algebraic Topology, Cambridge Univ. Press, 1980.
- Croom, F.H., Basic Concepts of Algebraic Topology, Springer-Verlag, 1978.