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
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
Review of basic point set topology (topological spaces,
continuous functions, Hausdorff spaces, compact spaces,
connected spaces etc.);
Product and quotient spaces;
Covering maps and the Monodromy Theorem;
The fundamental group of a topological space;
Free discontinuous group actions;
The topological classification of closed surfaces.
MA1214 (Introduction to Group Theory), and at least one of
MA2223 and MA2321.
This module will be examined in a 2-hour examination
in Trinity term.