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MA938 - Topics in Algebraic Topology

Lecturer: Emanuele Dotto

Term(s): Term 2

Commitment: 30 lectures

Assessment: Oral exam

Prerequisites: Basic knowledge of topological spaces and chain complexes, some familiarity with the language of category theory.

Content :

The aim of this module is to introduce the theory of model categories.

Model categories provide a general framework for homotopy theory, which allows to systematically study derived construction. The prime example is the homotopy theory of topological spaces, but there are many other examples, some of algebraic nature, such as the homotopy theory of chain complexes of modules over a ring.

In the module we will introduce model categories, set up some of these central examples, and study some of the fundamental constructions such as localisations, homotopy limits and colimits, and categories of monoids and their modules.

References:

▪ Hovey, Model Categories

▪ Hirschhorn, Model Categories and Their Localizations