Wolfson Lectures: The University of Manchester 4-10 January 2006

Topics and literature

To help Professor Shipley's potential audience to prepare for her talks, she has agreed to let us post an informal list of topics she hopes to cover, and literature that it would be worthwhile consulting in advance. She emphasises that none of this is definitive. We have summarised her suggestions below; any errors that might appear are entirely the fault of Nigel Ray!

In general terms, some familiarity with simplicial sets would help audience members maximise the benefit of the lectures. A good preparatory exercise in this regard is to understand the geometrical realisation of $\Delta[1] x \Delta[1])$!

Topics

As of 1st December, the following topics (at least) are on the menu.

• Definitions and Examples of Model Categories
• Brief introduction to simplicial sets
• The homotopy category
• Derived functors
• Creating new model categories from old
• Simplicial model categories
• Monoidal model categorie
• More applications

Literature

The following literature is relevant to the subject matter, with Dwyer and Spalinski (available online) probably a good place to start.

• Clemens Berger and Ieke Moerdijk. Axiomatic homotopy theory for operads. Comment. Math. Helv. Vol. 78(4):805--831
• A K Bousfield and Daniel M Kan. Homotopy Limits, Completions and Localizations. Lecture notes in Mathematics Volume 304. Springer Verlag, 1972.
• William G Dwyer and J Spalinski. Homotopy theories and model categories. In Ioan M James, editor, Handbook of Algebraic Topology, pages 73--126. Elsevier, 1995. http://www.math.uio.no/~paularne/SUPh05/DS.pdf
• Paul Goerss and Rick Jardine. Simplicial homotopy theory. Volume 174 of Progress in Mathematics. Birkhauser, 1999.
• Paul Goerss. Simplicial methods and model categories. http://jdc.math.uwo.ca/summerschool/
• Philip S Hirschhorn. Model Categories and Their Localizations. Volume 99 of Mathematical Surveys and Monographs, Amer. Math. Soc., Providence, R.I., 2003.
• Mark Hovey. Model Categories. Volume 63 of Mathematical Surveys and Monographs. Amer. Math. Soc., 1999.
• Mike Mandell. E-infinity Algebras and p-Adic Homotopy Theory, Topology 40(1):43--94 (2001).
• Mike Mandell. Cochains and Homotopy Type. math.AT/0311016
• Daniel Quillen. Homotopical Algebra. Lecture Notes in Mathematics Volume 43. Springer-Verlag, Berlin, 1967.
• Daniel Quillen. Rational homotopy theory, Annals of Math. 90(2):205--295, 1969.
• Stefan Schwede and Brooke Shipley. Algebras and modules in monoidal model categories. Proc. London Math. Soc.80:491-511, 2000. http://www.math.uic.edu/~bshipley/monoidal.pdf