Lectures on Homotopy Theory

The pdf files below are my lecture notes from a course on Homotopy Theory which I last gave at the University of Western Ontario during the Winter term of 2010.

The notes are subject to change - the indicated dates are last updates.

If you have comments or suggestions about these files, please do not hesitate to contact me: jardine@uwo.ca.

One comment: don't be misled by the link titles. These files are all worth two or more hours of class time.

• Lecture 001: Chain complexes (10/07/07)

• Lecture 002: Spaces (01/29/10)

• Lecture 003: Homotopical algebra (05/29/08)

• Lecture 004: Simplicial sets: examples and constructions, closed model structure (07/26/10)

• Lecture 005: Kan fibrations, simplicial sets and spaces (06/21/11)

• Lecture 006: Simplicial groups, simplicial modules, Eilenberg-Mac Lane spaces (03/10/10)

• Lecture 007: Properness, homotopy cartesian diagrams, diagrams of spaces, homotopy limits and colimits (06/21/11)

• Lecture 008: Bisimplicial sets, homotopy limits and colimits revisited, some applications: Quillen's Theorem B (04/23/10)

• Lecture 009: Bisimplicial abelian groups, derived functors for limit and colimit, spectral sequences, Eilenberg-Zilber Theorem, universal coefficients and Kunneth formula (06/30/11)

• Lecture 010: Fundamental groupoid, Serre spectral sequence, transgression, path-loop fibre sequence (06/21/11)

• Lecture 011: Postnikov towers, Hurewicz theorem, Freudenthal suspension theorem (11/08/07)

• References (03/19/10)