Description
The course starts with the basics of general topology. The fundamental group is then defined and studied, with an emphasis on examples: graphs and their fundamental groups, free groups, are especially motivating. Fundamental groups of general complexes are discussed, along with group presentations. Some applications will be given, such as winding number and the Brouwer Fixed point theorem. Students should finish the course able to compute: bases for the subgroup of a free group corresponding to an explicit covering space of a graph; presentations for fundamental groups of cell complexes; Cayley graphs of finite groups. The course could be taken as a complement to the course Algebraic Topology.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
Ìý