MTH649A - Algebraic Topology

Homotopy, Path homotopy. The fundamental group. Covering spaces. The fundamental group of the circle, S1, sphere, S2, Surfaces 2dimensional,Punctured plane etc. Techniques of calculation. The special Van Kampen theorem. Essential and Inessential maps Applications. The fundamental theorem of algebra, Browers fixed point theorem for the disc etc. Triangulations. Simplical complexes. Bary centric subdivision. Simplical mappings, The simplical approximation theorem. Simplical homology groups; Calculations for cone complex, Sn etc. The Euler Poincare formula. The Lefschetz fixed point theorem. Singular homology groups, Topological invariance. The exact homology sequence. The Eilenberg Steenrod axioms.