Proseminar on Algebraic Topology Fall 2007

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

Course Plan:

Here is a prelimilary schedule:

Thursday Sep 27th: Wall finiteness obstruction part I (Jim).
Tuesday Oct 2nd: Wall finiteness obstruction part II (Jim).
Thursday Oct 4th: ?
Tuesday Oct 9th: The EHP sequence and Samelson Whitehead products, part I (Niles and Justin).
Thursday Oct 11th: The EHP sequence and Samelson Whitehead products, part II (Niles and Justin).

List of possible topics

Unstable stuff:

Smith Theory
Hubbuck: If X is a homotopy commutative finite H-space then X is equivalent to a torus.
Wall's finiteness obstruction
Serre conjecture: finiteness of homotopy groups of spheres, except in certain dimensions.
U(\pi_* X \otimes Q) \simeq H_*(X;Q) for certain X.
The EHP sequence.
Samelson-Whitehead products.
Characteristic classes, cohomology of BU(n) etc.
Algebraic K-theory, BGL_n(\bar{F}_q) is equivalent to BU(n) after localizing at p.

Stable stuff:

K-theory and Hopf invariant 1.
K-theory and the Atiyah-Segal completion theorem.
Algebraic K-theory.
The Brown-Peterson spectrum
The homology of \Omega^n \Sigma^n X as a functor of the homology of X.

Previous Quarters:

Fall 2004 , Winter 2005 , Spring 2005 , Fall 2005 , Winter 2006 , Spring 2006 . Fall 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 Vigleik Angeltveit.
vigleik AT math.uchicago.edu.