An Invitation to Hyperbolic Groups

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

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The topic of this bookare hyperbolic groups in the sense of Gromov. These groups form one of the fundamental examples of study in geometric group theory. Fundamental examples include free groups and the fundamental groups of closed negatively curved manifolds. Hyperbolic groups capture the notion of negative curvature for discrete groups. This book starts with the basics, defining the groups and metric spaces of interest, and focussing on key examples (trees and free groups, and the hyperbolic plane and surface groups). It goes through the basic theory, providing an introduction to the basic ideas, results and constructions. In the second part of the book, more advanced and recent topicsare covered, in an attempt to bring the reader near to the modern research environment. A discussion of more general notions (coming from actions on delta-hyperbolic groups that are not proper and cocompact)is provided, and an indication of important and profitable directions for the futureis given.