Lectures on Homotopy Theory
The links below are to pdf files, which comprise the lecture notes for a course on Homotopy Theory.
This collection of files is the basic source material for the course, and the syllabus is listed on this page. All files are subject to revision as the course progresses.
More detail on topics covered here can be found in the Goerss-Jardine book Simplicial Homotopy Theory, which appears in the References file below.
The course will be given as a set of lectures at the University of Western Ontario, and will be available by video conference to students from other universities. Students from other sites can participate, from either traditional video conference rooms or by using personal computers. Please contact me if you wish to do so.
It would be quite helpful for a student to have a background in basic Algebraic Topology (our course Math 4152/9052) and/or Homological Algebra (our Math 9144) prior to taking this course.
Office: Middlesex College 118
Phone: 519-661-2111 x86512
This course will meet Monday, Wednesday and Friday, 12:30-13:30 EST, MC105C and online.
The first lecture will be on Monday, January 15.
Course Outline for Western Students: This is the OWL site for the course. Access it with your Western id. The syllabus is the same as below, but there is extra administrative information on the OWL site for Western students.
The main reference for the course is the Goerss-Jardine book "Simplicial Homotopy Theory". If your institution has the right kind of SpringerLink subscription (as does Western), you can download a pdf file for the book free of charge from the SpringerLink site, for example at this link. A (printed on demand) paper copy of the book is also available at subscribing institutions for a low fee.
Recordings of the lectures are available at this link.
The quality of the recordings is uneven. In particular, there is no sound for the first lecture, due to a hardware failure.
Part A: Homotopy theories
Lecture 01: Homological algebra
Lecture 02: Spaces
Lecture 03: Homotopical algebra
Lecture 04: Simplicial sets
Lecture 05: Fibrations, geometric realization
Lecture 06: Simplicial groups, simplicial modules
Lecture 07: Properness, diagrams of spaces
Lecture 08: Bisimplicial sets, homotopy limits and colimits
Lecture 09: Bisimplicial abelian groups, derived functors
Lecture 10: Serre spectral sequence, path-loop fibre sequence
Lecture 11: Postnikov towers, some applications
Lecture 13: Spectra and stable equivalence
Section 35: Cohomology
Section 36: Cup products
Section 37: Cohomology of cyclic groups
Section 38: Spectra
Section 39: Strict model structure
Section 40: Stable equivalences
Lecture 14: Basic properties
Lecture 15: Spectrum objects