02824nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018410000290020624500940023526000820032930000340041133600260044533700260047133800360049734700240053349000530055750600660061052015570067665000470223365000180228065000310229870000320232985600320236185600690239358-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070524sz fot ||| 0|eng d a978303719536970a10.4171/0362doi ach0018173 7aPBMP2bicssc a51-xxa53-xx2msc1 aBuyalo, Sergei,eauthor.10aElements of Asymptotic Geometryh[electronic resource] /cSergei Buyalo, Viktor Schroeder3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (212 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aAsymptotic 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.07aDifferential & Riemannian geometry2bicssc07aGeometry2msc07aDifferential geometry2msc1 aSchroeder, Viktor,eauthor.40uhttps://doi.org/10.4171/036423cover imageuhttps://www.ems-ph.org/img/books/schroeder_mini.jpg