Course Identification

Homotopies between continuous maps and homotopy equivalences.

CW complexes and their homotopical properties. 

Fundamental groups and covering spaces. 

 Higher homotopy groups, fibrations, Eilenberg McLane spaces, Postnikov tower. 

Homology and cohomology, long exact sequences in (co)homology, cup product.  

Poincare and Alexander dualities. 

Upon completion of the course the students are expected to be able to compute algebraic invariants of simple topological spaces (such as homology, homotopy, cohomology), and use them to tell apart non-homotopic maps and non-homotopy equivalent topological spaces. 

We will follow A. Hatcher's book "Algebraic Topology".