PMATH 467 - Algebraic Topology

We study algebraic structures which can be associated to topological spaces, and which are invariant under homotopy equivalence. Such topological invariants include homotopy groups, homology groups, and cohomology groups or rings. Possible applications include the classification of Platonic solids, the Brouwer and Lefschetz fixed-point theorems, the hairy ball theorem, the Borsuk-Ulam theorem, and the ham sandwich theorem.