On successful completion of this module, students will be able to:
describe the definitions and basic properties of products
and quotients of topological spaces;
describe in detail the construction of the fundamental group
of a topological space, and justify with reasoned logical
argument the manner in which topological properties of that
topological space are reflected in the structure of its
fundamental group;
justify with reasoned logical argument basic relationships
between the fundamental group of a topological space and the
covering maps for which that topological space is the base
space;
Module Content
Review of basic point set topology (topological spaces,
continuous functions, Hausdorff spaces, connected
spaces etc.);
Compact topological spaces;
Product and quotient spaces;
Covering maps and the Monodromy Theorem;
The fundamental group of a topological space;
Monodromy;
Free discontinuous group actions.
Module Prerequisite
MA1214 (Introduction to Group Theory), and at least one of
MA2223 and MA2321.
Assessment Detail
This module will be examined in a 2-hour examination
in Trinity term.