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Displaying 81 – 100 of 128

On irreducible, infinite, nonaffine Coxeter groups

Dongwen Qi (2007)

Fundamenta Mathematicae

The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. We also prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine...

On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier (2011)

Annales de l’institut Fourier

We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence $(G_{n})$ of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank $ω^{n}$ .

On the linearity problem for mapping class groups.

Brendle, Tara E., Hamidi-Tehrani, Hessam (2001)

Algebraic & Geometric Topology

On the residual properties of link groups.

Bardakov, V.G., Mikhajlov, R.V. (2007)

Sibirskij Matematicheskij Zhurnal

On the simple connectivity at infinity of groups

Daniele Ettore Otera (2003)

Bollettino dell'Unione Matematica Italiana

We study the simple connectivity at infinity of groups of finite presentation, and we give a geometric proof of its invariance under quasi-isometry in a special case.

One-relator groups and proper 3-realizability.

M. Cárdenas, F.F. Lasheras, A. Quintero, D. Repovs (2009)

Revista Matemática Iberoamericana

Optics in Croke-Kleiner Spaces

Fredric D. Ancel, Julia M. Wilson (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We explore the interior geometry of the CAT(0) spaces $X_{α} : 0 < α \leq π / 2$ , constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications....

OPTi's algorithm for discreteness determination.

Wada, Masaaki (2006)

Experimental Mathematics

Parabolic isometries of CAT(0) spaces and CAT(0) dimensions.

Fujiwara, Koji, Shioya, Takashi, Yamagata, Saeko (2004)

Algebraic & Geometric Topology

Presentations of surface braid groups by graphs

Paolo Bellingeri, Vladimir Vershinin (2005)

Fundamenta Mathematicae

We extend and generalise Sergiescu's results on planar graphs and presentations for the braid group Bₙ to other topological generalisations of Bₙ.

Preservation and Distortion of Area in Finitely Presented Groups.

S.M. Gersten (1996)

Geometric and functional analysis

Pro- $p$ groups and towers of rational homology spheres.

Boston, Nigel, Ellenberg, Jordan S. (2006)

Geometry & Topology

Productivity of the Zariski topology on groups

Dikran N. Dikranjan, D. Toller (2013)

Commentationes Mathematicae Universitatis Carolinae

This paper investigates the productivity of the Zariski topology $ℨ_{G}$ of a group $G$ . If $𝒢 = {G_{i} ∣ i \in I}$ is a family of groups, and $G = \prod_{i \in I} G_{i}$ is their direct product, we prove that $ℨ_{G} \subseteq \prod_{i \in I} ℨ_{G_{i}}$ . This inclusion can be proper in general, and we describe the doubletons $𝒢 = {G_{1}, G_{2}}$ of abelian groups, for which the converse inclusion holds as well, i.e., $ℨ_{G} = ℨ_{G_{1}} \times ℨ_{G_{2}}$ . If $e_{2} \in G_{2}$ is the identity element of a group $G_{2}$ , we also describe the class $Δ$ of groups $G_{2}$ such that $G_{1} \times {e_{2}}$ is an elementary algebraic subset of $G_{1} \times G_{2}$ for every group $G_{1}$ . We show among others, that $Δ$ is stable...

Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

Victor Gerasimov, Leonid Potyagailo (2013)

Journal of the European Mathematical Society

We describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using the Floyd completion we further prove that the property of relative hyperbolicity is invariant under quasi-isometric maps. If a finitely generated group $H$ admits a quasi-isometric map $ϕ$ into a relatively hyperbolic group $G$ then $H$ is itself relatively hyperbolic with respect to a system of subgroups whose image under $ϕ$ is situated within a uniformly bounded distance...

Regular neighbourhoods and canonical decompositions for groups.

Scott, Peter, Swarup, Gadde A. (2002)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Representations of polygons of finite groups.

Kapovich, Michael (2005)

Geometry & Topology

Resolutions of moduli spaces and homological stability

Oscar Randal-Williams (2016)

Journal of the European Mathematical Society

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.

Salvetti complex, spectral sequences and cohomology of Artin groups

Filippo Callegaro (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.

Self-embeddings of kleinian groups

Ken'ichi Ohshika, Leonid Potyagailo (1998)

Annales scientifiques de l'École Normale Supérieure

Small cancellation theory and automatic groups: Part II.

S.M. Gersten, H. Short (1991)

Inventiones mathematicae

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