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This paper compiles basic components of the construction of random groups and of the proof of their properties announced in [G10]. Justification of each step, as well as the interrelation between them, is straightforward by available techniques specific to each step. On the other hand, there are several ingredients that cannot be truly appreciated without(More)
This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α ≥ 1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study(More)
Nous présentons une approche asymptotiquè a la théorie de la petite simplification, et l'appliquonsà l'´ etude des groupes de Burnside libres. Abstract We present an asymptotic approach to small cancelation theory, and apply this method to the study of the free Burnside groups. The point of this article is to give a detailed account of the asymptotic(More)
Mathematics is about ”interesting structures”. What make a structure interesting is an abundance of interesting problems; we study a structure by solving these problems. The worlds of science, as well as of mathematics itself, is abundant with gems (germs?) of simple beautiful ideas. When and how may such an idea direct you toward beautiful mathematics? I(More)
We study fundamental groups of Kähler manifolds via their cuts or relative ends. 1. A group G is called Kähler if it serves as the fundamental group π 1 (V) of a compact Kähler manifold V. Equivalently, such a group G appears as a discrete free co-compact isometry group of a complete simply connected Kähler manifold X – the Galois group acting on the(More)