Goulnara Arzhantseva
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Goulnara Arzhantseva has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
- Ashot Minasyan
University of Southampton, United Kingdom
4 shared publications - Mark Sapir
Department of Mathematics, Vanderbilt University, Nashville, USA
3 shared publications - Victor Guba
Vologda State University 15 Lenin Street 160600 Vologda Russia
3 shared publications - Cornelia Drutu
Mathematical Institute; 24-29 St Giles Oxford OX1 3LB United Kingdom
2 shared publications - Ian James Leary
School of Mathematical Sciences, University of Southampton, Southampton, UK
2 shared publications - Jacek Świątkowski
Instytut Matematyczny, Uniwersytet Wrocławski, Wrocław, Poland
2 shared publications
Latest Publications
- Open Access
Infinite groups with fixed point properties
We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first examples of infinite finitely generated groups $Q$ with the property that for any action of $Q$ on any $X\in \mathcal{X}_{ac}$, there is a global fixed point. Moreover, $Q$ may be chosen to be simple and to have Kazhdan's property (T). We construct a finitely presented infinite group $P$ that admits no non-trivial action by diffeomorphisms on any smooth manifold in $\mathcal{X}_{ac}$. In building $Q$, we exhibit new families of hyperbolic groups: for each $n\geq 1$ and each prime $p$, we construct a non-elementary hyperbolic group $G_{n,p}$ which has a generating set of size $n+2$, any proper subset of which generates a finite $p$-group.Open AccessInfinite groups with fixed point properties
We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first examples of infinite finitely generated groups $Q$ with the property that for any action of $Q$ on any $X\in \mathcal{X}_{ac}$, there is a global fixed point. Moreover, $Q$ may be chosen to be simple and to have Kazhdan's property (T). We construct a finitely presented infinite group $P$ that admits no non-trivial action by diffeomorphisms on any smooth manifold in $\mathcal{X}_{ac}$. In building $Q$, we exhibit new families of hyperbolic groups: for each $n\geq 1$ and each prime $p$, we construct a non-elementary hyperbolic group $G_{n,p}$ which has a generating set of size $n+2$, any proper subset of which generates a finite $p$-group. - 5 February 2009
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 13 (3) , 1229-1263
Infinite groups with fixed point properties
- 5 February 2009
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 13 (3) , 1229-1263
Infinite groups with fixed point properties
- 1 January 2009
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2009 (633)
Compression functions of uniform embeddings of groups into Hilbert and Banach spaces
We construct finitely generated groups with arbitrary prescribed Hilbert space compression \alpha from the interval [0,1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 3, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (respectively, exact, of finite asymptotic dimension) with Hilbert space compression 0 are given. These groups are also the first examples of groups with uniformly convex Banach space compression 0
- 1 January 2009
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2009 (633)
Compression functions of uniform embeddings of groups into Hilbert and Banach spaces
We construct finitely generated groups with arbitrary prescribed Hilbert space compression \alpha from the interval [0,1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 3, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (respectively, exact, of finite asymptotic dimension) with Hilbert space compression 0 are given. These groups are also the first examples of groups with uniformly convex Banach space compression 0
- Open Access
Compression functions of uniform embeddings of groups into Hilbert and Banach spaces
We construct finitely generated groups with arbitrary prescribed Hilbert space compression \alpha from the interval [0,1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 3, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (respectively, exact, of finite asymptotic dimension) with Hilbert space compression 0 are given. These groups are also the first examples of groups with uniformly convex Banach space compression 0.
Open AccessCompression functions of uniform embeddings of groups into Hilbert and Banach spaces
We construct finitely generated groups with arbitrary prescribed Hilbert space compression \alpha from the interval [0,1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 3, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (respectively, exact, of finite asymptotic dimension) with Hilbert space compression 0 are given. These groups are also the first examples of groups with uniformly convex Banach space compression 0.
- Open Access
The SQ-universality and residual properties of relatively hyperbolic groups
We study residual properties of relatively hyperbolic groups. In particular, we show that if a group $G$ is non-elementary and hyperbolic relative to a collection of proper subgroups, then $G$ is SQ-universal.Open AccessThe SQ-universality and residual properties of relatively hyperbolic groups
We study residual properties of relatively hyperbolic groups. In particular, we show that if a group $G$ is non-elementary and hyperbolic relative to a collection of proper subgroups, then $G$ is SQ-universal. - 8 December 2006
- Published by Springer Nature in Geometriae Dedicata
- Vol. 124 (1) , 5-26
The true prosoluble completion of a group: Examples and open problems
- 8 December 2006
- Published by Springer Nature in Geometriae Dedicata
- Vol. 124 (1) , 5-26
The true prosoluble completion of a group: Examples and open problems
- Open Access
The true prosoluble completion of a group: examples and open problems
The true prosoluble completion $P\Cal S (\Gamma)$ of a group $\Gamma$ is the inverse limit of the projective system of soluble quotients of $\Gamma$. Our purpose is to describe examples and to point out some natural open problems. We discuss a question of Grothendieck for profinite completions and its analogue for true prosoluble and true pronilpotent completions. 1. Introduction. 2. Completion with respect to a directed set of normal subgroups. 3. Universal property. 4. Examples of directed sets of normal subgroups. 5. True prosoluble completions. 6. Examples. 7. On the true prosoluble and the true pronilpotent analogues of Grothendieck's problem.Open AccessThe true prosoluble completion of a group: examples and open problems
The true prosoluble completion $P\Cal S (\Gamma)$ of a group $\Gamma$ is the inverse limit of the projective system of soluble quotients of $\Gamma$. Our purpose is to describe examples and to point out some natural open problems. We discuss a question of Grothendieck for profinite completions and its analogue for true prosoluble and true pronilpotent completions. 1. Introduction. 2. Completion with respect to a directed set of normal subgroups. 3. Universal property. 4. Examples of directed sets of normal subgroups. 5. True prosoluble completions. 6. Examples. 7. On the true prosoluble and the true pronilpotent analogues of Grothendieck's problem. - Open Access
Relatively Hyperbolic Groups are $C^*$-simple
We characterize relatively hyperbolic groups whose reduced $C^*$-algebra is simple as those, which have no non-trivial finite normal subgroups.
Open AccessRelatively Hyperbolic Groups are $C^*$-simple
We characterize relatively hyperbolic groups whose reduced $C^*$-algebra is simple as those, which have no non-trivial finite normal subgroups.
- Open Access
Testing Cayley graph Densities (version longue)
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson's group F. The sign means that we would like you to check our changes here. ♠
Open AccessTesting Cayley graph Densities (version longue)
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson's group F. The sign means that we would like you to check our changes here. ♠
- Open Access
Metrics on diagram groups and uniform embeddings in a Hilbert space
We give first examples of finitely generated groups having an intermediate, with values in (0,1), Hilbert space compression (which is a numerical parameter measuring the distortion required to embed a metric space into Hilbert space). These groups include certain diagram groups. In particular, we show that the Hilbert space compression of Richard Thompson's group $F$ is equal to 1/2, the Hilbert space compression of the restricted wreath product $Z\wr Z$ is between 1/2 and 3/4, and the Hilbert space compression of $Z\wr (Z\wr Z)$ is between 0 and 1/2. In general, we find a relationship between the growth of $H$ and the Hilbert space compression of $Z\wr H$.Open AccessMetrics on diagram groups and uniform embeddings in a Hilbert space
We give first examples of finitely generated groups having an intermediate, with values in (0,1), Hilbert space compression (which is a numerical parameter measuring the distortion required to embed a metric space into Hilbert space). These groups include certain diagram groups. In particular, we show that the Hilbert space compression of Richard Thompson's group $F$ is equal to 1/2, the Hilbert space compression of the restricted wreath product $Z\wr Z$ is between 1/2 and 3/4, and the Hilbert space compression of $Z\wr (Z\wr Z)$ is between 0 and 1/2. In general, we find a relationship between the growth of $H$ and the Hilbert space compression of $Z\wr H$.