# Book Details

Search page | Title Index | Author Index

Preface | Table of Contents | MARC record | Metadata XML | e-Book PDF (1207 KB)*Sergei Buyalo (Steklov Institute of Mathematics, St. Petersburg, Russia)*

Viktor Schroeder (University of Zurich, Switzerland)

Viktor Schroeder (University of Zurich, Switzerland)

#### Elements of Asymptotic Geometry

ISBN print 978-3-03719-036-4, ISBN online 978-3-03719-536-9DOI 10.4171/036

May 2007, 212 pages, hardcover, 16.5 x 23.5 cm.

58.00 Euro

Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely encoded in the boundary at infinity.

In the first part of this book, in analogy with the
concepts of classical hyperbolic geometry, the authors provide a systematic
account of the basic theory
of Gromov hyperbolic spaces. These spaces have been studied extensively
in the last twenty years, and have found applications in group theory,
geometric topology, Kleinian groups, as well as dynamics and rigidity theory.
In the second part of the book, various
aspects of the asymptotic geometry of arbitrary metric spaces are considered.
It turns out that the boundary at infinity approach is not appropriate in the general case,
but dimension theory proves useful for finding interesting results and applications.

The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory.

The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich. It addressed to graduate students and researchers working in geometry, topology, and geometric group theory.