Description
Deductive Press Introduction to Arithmetic Groups by Dave Witte Morris
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 Ratners 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 Qrank ergodic theory unitary representations amenability Kazhdans property (T) and quasiisometries. Numerous exercises enhance the books usefulness both as a textbook for a secondyear graduate course and for selfstudy. 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.show more