Introduction to Algebraic K-Theory I

Content

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Description

Time: Wednesdays 11.00 - 13.00 

Location for Maxwell Institute students: Bayes Centre (room 5.46)

Module Leader: Irakli Patchokoria (University of Aberdeen)

Module Summary

These lectures give a basic introduction to the algebraic K-theory space K(R) without assuming much knowledge in category theory or homotopy theory. The work is divided into two parts. Semester I introduces all the necessary tools from category theory and simplicial homotopy theory which one needs to define the K-theory space. Semester II defines K(R) and studies the basic properties of these spaces. While many textbooks cover the classical material in algebraic K-theory, these lectures offer an accessible introduction to this active area of research for graduate students. One can also view these lectures as an introduction to the use of categories in homotopy theory, or rather the interaction between the two areas of mathematics. The main reference is the book by Madsen and Patchkoria which will be available to download. It also contains exercises which we will use.

Assessment

4 Homeworks, each 25%