Algebraic Topology
Content
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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.