Introduction to
Arithmetic
Groups
by Dave Witte Morris
Click
HERE for PDF file of a draft of the chapters that have been written so
far.
Here are the chapters in the current version:
- What is a Locally Symmetric Space?
- Geometric Meaning of R-rank and Q-rank
- Introduction to Semisimple Lie Groups
- Basic Properties of Lattices
- What is an Arithmetic Lattice?
- Examples of Lattices
- Real Rank
- Q-rank
- Ergodic Theory
- Amenable Groups
- Kazhdan's Property (T)
- Margulis Superrigidity Theorem
- Normal Subgroups of Gamma
- <not written yet>
- Arithmetic Lattices in Classical Groups
- Appendices:
- Assumed Background
- Which Classical Groups are Isogenous?
- Central Division Algebras over Number Fields
This version was posted April 6, 2008, and has several new
chapters. I hope that the book will be fairly complete (though
perhaps not polished) sometime in the next few months.
The Latex source files are available at http://arxiv.org/abs/math/0106063
Some additional chapters are in development, including "Reduction
Theory: A Weak Fundamental Domain for G/Gamma," "Ratner's Theorems on
Unipotent Flows," and "Why GZ is
a Lattice in G." Here is the current version of one of them: