Algebraic Topology


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Module Overview: Algebraic Topology

This module is intended to give an overview of basic concepts, examples and techniques in algebraic topology. 

Lectures [Thursdays, 13:00-15:00]

Provisional programme:

  • Lecture 1: Basic examples and constructions of topological spaces.
  • Lecture 2: Manifolds, basic homotopy theory and homotopy groups.
  • Lecture 3: Cofibrations, cell attachments and CW-complexes.
  • Lecture 4: Cellular approximation and relative homotopy groups.
  • Lecture 5: Fibre bundles, fibrations and the Hopf map.
  • Lecture 6: An introduction to homology.
  • Lecture 7: Homotopy invariance, exactness and excision.
  • Lecture 8: Computations and applications of homology.
  • Lecture 9: An introduction to cohomology
  • Lecture 10: Further topics in cohomology theory


This module is assessed in two assignments.


Working knowledge of metric and topological spaces, linear algebra and basic group theory (groups and group actions).


The Team