Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...
We propose elementary and explicit presentations of groups that have no amenable quotients and yet are SQ-universal. Examples include groups with a finite K (pi,1), no Kazhdan subgroups and no Haagerup quotients. ...
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Mobius group of the projective line. Since the general proof is very simple but not explicit, we also provi ...
We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover gi ...
Non-positively curved spaces admitting a cocompact isometric action of an amenable group are investigated. A classification is established under the assumption that there is no global fixed point at infinity under the full isometry group. The visual bounda ...
Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-iso ...
We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions, related among others to a problem studied by Reiter in 19 ...
Let G be any group containing an infinite elementary amenable subgroup and let 2 < p < infinity. We construct an exhaustion of l(p) G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obst ...
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...
Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...
Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor Z-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the negative by prod ...
The group of piecewise projective homeomorphisms of the line provides straightforward torsion-free counterexamples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established. ...
We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suita ...
It is a well-known open problem since the 1970s whether a finitely generated perfect group can be normally generated by a single element or not. We prove that the topological version of this problem has an affirmative answer as long as we exclude infinite ...
We prove that the norm of the Euler class E for flat vector bundles is 2−n (in even dimension n, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...
We prove a fixed point theorem for a family of Banach spaces, notably for L^1. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. ...
Let Gamma be an irreducible lattice in a product of n infinite irreducible complete Kac–Moody groups of simply laced type over finite fields. We show that if n>2, then each Kac–Moody groups is in fact a simple algebraic group over a local field and Gamma i ...
Recall that a rng is a ring which is possibly non-unital. In this note, we address the problem whether every finitely generated idempotent rng (abbreviated as irng) is singly generated as an ideal. It is well-known that it is the case for a commutative irn ...
We present a contribution to the structure theory of locally compact groups. The emphasis is put on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic cocompact sub ...
