Scottish Mathematical Sciences Training Centre

Theme: Structure and symmetry
Theme head: Professor Ivan Cheltsov

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, 11.10.2018: Basic examples and constructions of topological spaces.
• Lecture 2, 18.10.2018: Manifolds, basic homotopy theory and homotopy groups.
• Lecture 3, 25.10.2018: Cofibrations, cell attachments and CW-complexes.
• Lecture 4, 01.11.2018: Cellular approximation and relative homotopy groups.
• Lecture 5, 08.11.2018: Fibre bundles, fibrations and the Hopf map.
• Lecture 6, 15.11.2018: An introduction to homology.
• Lecture 7, 22.11.2018: Homotopy invariance, exactness and excision.
• Lecture 8, 29.11.2018: Computations and applications of homology.
• Lecture 9, 06.12.2018: An introduction to cohomology
• Lecture 10, 13.12.2018: Further topics in cohomology theory

Assessment 

• Assignment 1 is due on Friday November 30th, 2018
• Assignment 2 is due on Tuesday December 18th, 2018

Prerequisites

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