Algebraic Topology II

This course is a continuation of algebraic topolgy I, one could however take algebraic topologly II with a good background from Analysis I-III and linear algebra I, with some additional outside work to assimilate some basic material from algebraic topolgy I. We will also review some important topics from algebraic Topology I, such as the theory of chain complexes and homology.

 

The main topics covered will be cohomology, homotopy theory and how one uses cohomological invariants to compute homotopy groups. We will also discuss such algebraic topics as spectral sequences and the Steenrod algebra. We will use Hatcher's "Algebraic Topology" Chapters 3 and 4, as our main text.

 

Text

Hatcher, Allen, Algebraic topology. Cambridge University Press, Cambridge, 2002. xii+544 pp.