Module MA342R: Covering Spaces and Fundamental Groups

Credit weighting (ECTS)

5 credits

Semester/term taught

Michaelmas term 2016-17

Contact Hours

11 weeks, 3 lectures including tutorials per week

Lecturer

Prof. David Wilkins

Learning Outcomes

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