Math 290 reading seminar: GKM theory.
GKM theory, put in its current form by Goresky, Kottwicz, and
Macpherson (hence the name), is a way of calculating topological
invariants of a space with a torus action by doing combinatorics on a
graph drawn in a vector space. The plan is to read Macpherson's notes
on the subject from the lectures he gave at PCMI four summers ago. I
anticipate this will take almost the entire quarter.
The tentative meeting time is 4-6 on Mondays. Since I will be out of
town on January 7, there will be no meeting that day, and we will have
a brief organizational meeting at 4:15 on Wednesday, January 9.
The main reference will be:
- R. Macpherson, Equivariant Invariants and Linear Geometry, in
_Geometry Combinatorics_, IAS/Park City Mathematics series 13 (2004),
319--388.
I have made a photocopy of the article and placed it in MY mailbox on
the first floor. Please make yourself a copy and return that copy to
my mailbox for others.
More references can be found in Macpherson's bibliography, and some
other interesting papers are:
- T. Braden, L. Chen, and F. Sottile, The equivariant Chow rings of
quot schemes, arXiv:math/0602161
- J. Tymoczko, An introduction to equivariant cohomology and
homology following Goresky, Kottwitz, and MacPherson,
arXiv:math/0503369
- J. Tymoczko, Permutation actions on equivariant cohomology,
arXiv:math/0706.0460
- Z. Yun, Goresky-Macpherson calculus for the affine flag varieties,
arXiv:math/0712.4395