Algebraic Topology

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Description

Thursday 13.00-15.00

Module Overview: Algebraic Topology

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

Lectures 

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

Assessment 

This module is assessed in two assignments, each equally weighted to be worth 50% of the Final Grade. 

Assignment 1: will be released after the lecture in week 5.

Assignment 2: will be released at the end of the module.