Deductive Press

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.

The PDF has also been permanently archived at
http://arxiv.org/src/math/0106063/anc/     (external links open in a new window)

The Latex source files are available at
http://arxiv.org/abs/math/0106063

Inexpensive printed copies of the book are also available.
• The book is on Amazon and Barnes and Noble, with the paperback priced at $11 (and the hardcover at$17) plus shipping (as of February 2019).  It may also be available from other online booksellers.

• The paperback and hardcover are both listed in Books in Print, so your local bookstore should be able to special-order a copy for you from the distributor (Ingram Book Company).  To cover their costs, the bookstore will probably need to charge a few dollars more than the above-mentioned online sellers.  (At the industry-standard markup, the paperback would sell for about $18 and the hardcover for about$30.)

• Foreign readers: The paperback has been seen on amazon.co.uk for £8.50, and on amazon.de for EUR 10,40.

Errata:

• page xii: The name of Hugh Thomas is misspelled in line 7 of the acknowledgments.

• page 109: A reference should have been given for Exercise 5.2#4. It is Theorem 2 of [A. Borel, Density and maximality of arithmetic subgroups, J. Reine Angew. Math. 224 (1966) 78-89. MR0205999]. (Thanks to Uri Bader for pointing out the omission.)

• page 137: Change $\mathrm{diag}(\omega, 1, \omega^{-1})$ to $\mathrm{diag}(\omega, \omega^{-2}, \omega)$. (Thanks to Sebastian Hurtado for pointing out the error.)