Cohomology of Manifolds and Groups
This course is a sequel to `Introduction to Algebraic Topology'
Review of singular homology; Cohomology groups; Cup and Cap products.
CW complexes, Homotopy groups and Hurewicz theorem.
Whitehead's theorem , obstruction theory for CW complexes
Poincare duality and other duality theorems, Applications.
Homological Algebra: Free and Projective resolutions, cohomology
and homology groups of a module.
Cohomology of groups and applications: cohomological dimension,
group actions on spheres.
Books
- Hatcher, A., Algebraic topology. Cambridge University Press, Cambridge, 2002.
- Brown, K. S., Cohomology of Groups, Springer Verlag Graduate
Texts in Mathematics 87, 1982.