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, compact spaces,
connected spaces etc.);

Product and quotient spaces;

Covering maps and the Monodromy Theorem;

The fundamental group of a topological space;

Monodromy;

Free discontinuous group actions;

The topological classification of closed surfaces.

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.