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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
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
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.