Introduction to Arithmetic
Groups
Dave Witte Morris
ISBN: 978-0-9865716-0-2 (paperback)
978-0-9865716-1-9 (hardcover)
This book provides a gentle introduction to the study of arithmetic
subgroups of semisimple Lie groups. This means that the goal is to
understand the group SL(n,Z) and certain of its subgroups. Among the major
results discussed in the later chapters are the Mostow Rigidity Theorem,
the Margulis Superrigidity Theorem, Ratner's Theorems, and the
classification of arithmetic subgroups of classical groups. As background
for the proofs of these theorems, the book provides primers on lattice
subgroups, arithmetic groups, real rank and Q-rank, ergodic theory,
unitary representations, amenability, Kazhdan's property (T), and
quasi-isometries. Numerous exercises enhance the book's usefulness both as
a textbook for a second-year graduate course and for self-study. In
addition, notes at the end of each chapter have suggestions for further
reading. (Proofs in this book often consider only an illuminating special
case.) Readers are expected to have some acquaintance with Lie groups, but
appendices briefly review the prerequisite background. A PDF file of the
book is available on the internet. This inexpensive printed edition is for
readers who prefer a hardcopy.
Download a free PDF file of this 492-page book by clicking
HERE.
(The PDF file has only 491 pages, but the official length of the book is
492 pages, because an extra page is added at the end for a barcode during
the printing process.)
The current version is 1.0 of April 2015.
Errata: