144 citations · 202 across the 16 of their papers we have counts for
16 papers
Spectra of infinite Cayley graphs, examples with pure band spectra
Pierre de la Harpe
It is shown that there are groups with finite generating sets such that the adjacency operator of the Cayley graph is a disjoint union of intervals, fo…
Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs
Pierre de la Harpe
The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity functio…
Spectral measures and dominant vertices in graphs of bounded degree
Claire Bruchez, Pierre de la Harpe, Tatiana Nagnibeda
A graph of bounded degree has an adjacency operator~ which acts on the Hilbert space . There are different kinds of measures of interest on the spectrum…
On the prehistory of growth of groups
Pierre de la Harpe
The subject of growth of groups has been active in the former Soviet Union since the early 50's and in the West since 1968, when articles of Švarc and Milnor have been published, i…
Brouwer degree, domination of manifolds, and groups presentable by products
Pierre de la Harpe
For oriented connected closed manifolds of the same dimension, there is a transitive relation: dominates , or , if there exists a continuous map of non-zero degree…
Presentability by products for some classes of groups
P. de la Harpe, D. Kotschick
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuti…
Amenability and ergodic properties of topological groups: from Bogolyubov onwards
Rostislav Grigorchuk, Pierre de la Harpe
The purpose of this expository article is to revisit the notions of amenability and ergodicity, and to point out that they appear for topological groups that are not necessarily lo…
Metric geometry of locally compact groups
Yves Cornulier, Pierre de la Harpe
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 ob…
Amenable groups without finitely presented amenable covers
Mustafa Gokhan Benli, Rostislav Grigorchuk, Pierre De La Harpe
The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups with the fol…
The Fuglede-Kadison determinant, theme and variations
Pierre de la Harpe
We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in B…
Groups with faithful irreducible projective unitary representations
Bachir Bekka, Pierre de la Harpe
For a countable group G and a multiplier c on G with values in the circle, we study the property of G having a unitary projective c-representation which is both irreducible and pro…
Topologie, théorie des groupes et problèmes de décision. Célébration d'un article de Max Dehn de 1910
Pierre de la Harpe
This paper, in French, is a celebration of Max Dehn, and an essay of describing some of his results published in the beginning of the 1910's, and their offspring. It has been writt…
C-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds
Pierre de la Harpe, Jean-Philippe Préaux
We establish sufficient conditions for the C-simplicity of two classes of groups. The first class is that of groups acting on trees, such as amalgamated free products, HNN-exte…
Representation zeta functions of wreath products with finite groups
Laurent Bartholdi, Pierre de la Harpe
Let G be a group which has for all n a finite number r_n(G) of irreducible complex linear representations of dimension n. Let be its re…
Irreducibly represented groups
Bachir Bekka, Pierre de la Harpe
A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which gener…
Groupes fondamentaux des varietes de dimension 3 et algebres d'operateurs
Pierre de la Harpe, Jean-Philippe Preaux
We provide a geometric characterization of manifolds of dimension 3 with fundamental groups of which all conjugacy classes except 1 are infinite, namely of which the von Neumann al…