Systolic invariants of groups and $2$-complexes via Grushko decomposition

Yuli B. Rudyak; Stéphane Sabourau

Displaying similar documents to “Systolic invariants of groups and $2$ -complexes via Grushko decomposition”

Combinatorial and group-theoretic compactifications of buildings

Pierre-Emmanuel Caprace, Jean Lécureux (2011)

Annales de l’institut Fourier

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Let $X$ be a building of arbitrary type. A compactification $𝒞_{sph} (X)$ of the set ${Res}_{sph} (X)$ of spherical residues of $X$ is introduced. We prove that it coincides with the horofunction compactification of ${Res}_{sph} (X)$ endowed with a natural combinatorial distance which we call the . Points of $𝒞_{sph} (X)$ admit amenable stabilisers in $Aut (X)$ and conversely, any amenable subgroup virtually fixes a point in $𝒞_{sph} (X)$ . In addition, it is shown that, provided $Aut (X)$ is transitive enough, this compactification also coincides with the group-theoretic...

On the Fundamental Group of self-affine plane Tiles

Jun Luo, Jörg M. Thuswaldner (2006)

Annales de l’institut Fourier

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Let $A \in ℤ^{2} \times ℤ^{2}$ be an expanding matrix, $𝒟 \subset ℤ^{2}$ a set with $| det (A) |$ elements and define $𝒯$ via the set equation $A 𝒯 = 𝒯 + 𝒟$ . If the two-dimensional Lebesgue measure of $𝒯$ is positive we call $𝒯$ a self-affine plane tile. In the present paper we are concerned with topological properties of $𝒯$ . We show that the fundamental group $π_{1} (𝒯)$ of $𝒯$ is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of $π_{1} (𝒯)$ . Furthermore, we give a short proof of the fact that the closure of each component...

On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier (2011)

Annales de l’institut Fourier

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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 $ω^{n}$ .

Billiard complexity in the hypercube

Nicolas Bedaride, Pascal Hubert (2007)

Annales de l’institut Fourier

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We consider the billiard map in the hypercube of $ℝ^{d}$ . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that $n^{3 d - 3}$ is the order of magnitude of the complexity.

Generalized Staircases: Recurrence and Symmetry

W. Patrick Hooper, Barak Weiss (2012)

Annales de l’institut Fourier

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We study infinite translation surfaces which are $ℤ$ -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Displaying similar documents to “Systolic invariants of groups and 2 -complexes via Grushko decomposition”

Combinatorial and group-theoretic compactifications of buildings

On the Fundamental Group of self-affine plane Tiles

On the Cantor-Bendixson rank of metabelian groups

Billiard complexity in the hypercube

Generalized Staircases: Recurrence and Symmetry

Displaying similar documents to “Systolic invariants of groups and $2$ -complexes via Grushko decomposition”