AMAT 840: Topics in Topology Fall 2013
|Class hours||MWF 10:2511:20am|
|Office||Earth Science 120B|
|Office hours||M 11:30am12:30pm and WF 1:30pm2:30pm|
|Email address||bgoldfarb at albany.edu|
The goal will be to learn the necessary background from algebraic geometry, the theory of linear and arithmetic groups, homology and cohomology, in order to read to reasonable depth the classical paper by A. Borel and J.-P. Serre, Corners and arithmetic groups,
Comment. Math. Helv. No.48 (1973), 436-491.
I will post the material used to prepare for class and occasionally my own notes on this page.
0) It seems that the paper of Borel and Serre is not available for free download, even with the subscriptions that the University Library owns, but here is apparently a way to read the paper online. On that page, follow the link under "Access Full Article" header.
1) Here is the first post with a great resource on arithmetic groups that contains much much more than we will need and use: Introduction to arithmetic groups by Dave Witte-Morris.
2) Well, this is a link to the 2008 workshop on The Isoperimetric Inequality for SL(n,Z) at AIM. It's about geometric properties of arithmetic and related groups. It seems to have given a lot of inspiration to those who attended.
3) The first chapter of Daniel Bump's book Algebraic Geometry.
4) Notes on The Grassmannian as a Projective Variety.
5) The full copy of Corners and Arithmetic Groups.
6) The photo of Borel and Serre (Borel on the right, Serre on the left).
The following information is added to satisfy the Minimum Contents of a Class Syllabus requirements. The prerequisites for this course are first year courses in algebra and topology. The course is A-E graded. There is no official textbook. Attendance is critical to success in the class.