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.