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)