Proseminar on Algebraic Topology Spring 2006

Instructor: Peter May
Website: www.math.uchicago.edu/~fiore/1/proseminar.html
Time and Place: Tuesdays and Thursdays 1:30-3:00 in Eckhart Room 203
Audience: Graduate students in their second year or higher, with an interest in algebraic topology.
Email List: http://zaphod.uchicago.edu:8080/mailman/listinfo/topology

Course Plan:

Peter May will give an informal introduction to stable homotopy theory and the category of spectra.
No prerequisites.
Stable homotopy theory is that branch of algebraic topology that deals with phenomena that are stable under suspension. It includes all of homology and cohomology theory, for example. We'll begin at the beginning, following an historical route: ordinary homology and cohomology, duality, cobordism theory, K-theory, and the search for a good stable homotopy category of spectra (that gets us to 1964). We will digress to operads, infinite loop space theory and algebraic K-theory (the 1970's), and then return to an introduction to modern stable homotopy theory. This begins with the discovery of symmetric monoidal categories of spectra that allow one to import methods of ring theory, derived homological algebra, and algebraic geometry into stable homotopy theory.

References:

May, J. P. Stable algebraic topology, 1945--1966. History of topology, 665--723, North-Holland, Amsterdam, 1999.

Previous Quarters:

Fall 2004 , Winter 2005 , Spring 2005 , Fall 2005 , Winter 2006 .

Other Stuff:

For inspiration here's a link to the student topology seminar "babytop" at MIT , the student topology reading seminar "juvitop" at MIT and the Kan seminar .

This site is based on Jespers old site, and is maintained by Tom Fiore.
fiore AT math.uchicago.edu.