The purpose of this book is to describe the global properties of complete simply connected
spaces that are non-positively curved in the sense of AD Alexandrov and to examine the …

The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

This book offers to study locally compact groups from the point of view of appropriate metrics
that can be defined on them, in other words to study" Infinite groups as geometric objects" …

In this book, we present important recent results on the geometry and topology of 3-
dimensional manifolds and orbifolds. Orbifolds are natural generalizations of manifolds, and …

In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME
was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in …

In Gr1], Gr2] Gromov proposes and studies the problem of classifying nitely generated
groups up to quasi-isometry. On the one hand this has motivated an industry of producing …

In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of
finitely generated groups. In particular, we answer a question of Woess and prove a …

Geometric group theory has made remarkable progress in the last decade, producing a
wealth of striking and deep results which incorporate a wide range of mathematical tools …

The title refers to the area of research which studies infinite groups using measure-theoretic
tools, and studies the restrictions that group structure imposes on ergodic theory of their …

In this article we survey recent progress on quasi-isometric rigidity of polycyclic groups.
These results are contributions to Gromov's program for classifying finitely generated groups …