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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]
- 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).
- Lectures 1-5: Alessandro Sisto (A.firstname.lastname@example.org)
- Lectures 6-10: Dinakar Muthiah (email@example.com)