Algebraic topology is about associating algebraic structures (for example, groups) to topological spaces in such a way that continuous mappings naturally give rise to homomorphisms between the associated algebraic objects. Intractable topological problems (like determining the maximum number of linearly independent tangent vector fields on a sphere of given dimension) can be translated into algebraic problems and solved by exploiting the greater rigidity of algebraic structures. The course begins by establishing the combinatorial classification of surfaces and uses this as a readily accessible context for introducing some basic ideas of algebraic topology. It then develops the fundamental aspects of homotopy and homology theories.

Note: Students wishing to enrol in Level III Higher Pure Mathematics courses should consult with the Pure Mathematics Department before enrolling.