Equivalence relations induced by some locally compact groups of homeomorphisms of $2^{ℕ}$

B. Majcher-Iwanow

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Displaying similar documents to “Equivalence relations induced by some locally compact groups of homeomorphisms of $2^{ℕ}$ ”

For Coxeter groups $z^{| g |}$ is a coefficient of a uniformly bounded representation

Tadeusz Januszkiewicz (2002)

Fundamenta Mathematicae

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We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.

Non-locally compact Polish groups and two-sided translates of open sets

Maciej Malicki (2008)

Fundamenta Mathematicae

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This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of $S_{\infty}$ in terms of group actions, and prove that certain natural classes of...

On some spaces of linear functionals on the algebras $A_{p} (G)$ for locally compact groups

E. E. Granirer (1987)

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On finite groups acting on a connected sum of 3-manifolds S² × S¹

Bruno P. Zimmermann (2014)

Fundamenta Mathematicae

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Let $H_{g}$ denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on $H_{g}$ which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on $H_{g}$ which is quadratic in g. For the proofs we develop a calculus...

Shadowing in actions of some Abelian groups

Sergei Yu. Pilyugin, Sergei B. Tikhomirov (2003)

Fundamenta Mathematicae

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We study shadowing properties of continuous actions of the groups $ℤ^{p}$ and $ℤ^{p} \times ℝ^{p}$ . Necessary and sufficient conditions are given under which a linear action of $ℤ^{p}$ on $ℂ^{m}$ has a Lipschitz shadowing property.

The local weight of an effective locally compact transformation group and the dimension of $L^{2} (G)$

J. de Vries (1978)

Colloquium Mathematicae

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Shadowing in multi-dimensional shift spaces

Piotr Oprocha (2008)

Colloquium Mathematicae

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We show that the class of expansive $ℤ^{d}$ actions with P.O.T.P. is wider than the class of actions topologically hyperbolic in some direction $ν \in ℤ^{d}$ . Our main tool is an extension of a result by Walters to the multi-dimensional symbolic dynamics case.

Topological friction in aperiodic minimal $ℝ^{m}$ -actions

Jarosław Kwapisz (2010)

Fundamenta Mathematicae

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For a continuous map f preserving orbits of an aperiodic $ℝ^{m}$ -action on a compact space, its displacement function assigns to x the “time” $t \in ℝ^{m}$ it takes to move x to f(x). We show that this function is continuous if the action is minimal. In particular, f is homotopic to the identity along the orbits of the action.

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

Coxeter group actions on the complement of hyperplanes and special involutions

Giovanni Felder, A. Veselov (2005)

Journal of the European Mathematical Society

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We consider both standard and twisted actions of a (real) Coxeter group $G$ on the complement $ℳ_{G}$ to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in $G$ and give explicit formulae which describe both actions on the total cohomology $H^{*} (ℳ_{G}, 𝒞)$ in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group $S_{n}$ , the...

Non-orbit equivalent actions of $𝔽_{n}$

Adrian Ioana (2009)

Annales scientifiques de l'École Normale Supérieure

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For any $2 \leq n \leq \infty$ , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $𝔽_{n}$ . These actions arise as diagonal products between a generalized Bernoulli action and the action $𝔽_{n} ↷ (𝕋^{2}, λ^{2})$ , where $𝔽_{n}$ is seen as a subgroup of ${SL}_{2} (ℤ)$ .

Homogenization of codimension 1 actions of $ℝ^{n}$ near a compact orbit

Marcos Craizer (1994)

Annales de l'institut Fourier

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Let $Φ$ be a $C^{\infty} ℝ^{n}$ -action on an orientable $(n + 1)$ -dimensional manifold. Assume $Φ$ has an isolated compact orbit $T$ and let $W$ be a small tubular neighborhood of it. By a $C^{\infty}$ change of variables, we can write $W = ℝ^{n} / ℤ^{n} \times I$ and $T = 𝕋^{n} \times [0]$ , where $I$ is some interval containing 0. In this work, we show that by a $C^{0}$ change of variables, $C^{\infty}$ outside $T$ , we can make $Φ_{| W}$ invariant by transformations of the type $(x, z) \to (x + a, z), a \in ℝ^{n}$ , where $x \in ℝ^{n} / ℤ^{n}$ and $z \in I$ . As a corollary one cas describe completely the dynamics of $Φ$ in $W$ .

The orbits of the Hurwitz action of the braid groups on the standard generators

Yoshiro Yaguchi (2010)

Fundamenta Mathematicae

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The Hurwitz action of the n-braid group Bₙ on the n-fold direct product $(B_{m}) ⁿ$ of the m-braid group $B_{m}$ is studied. We show that the orbit of any n- tuple of the n standard generators of $B_{n + 1}$ consists of the (n-1)th powers of n+1 elements.

Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

Victor Gerasimov, Leonid Potyagailo (2013)

Journal of the European Mathematical Society

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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...

Compactifications of ℕ and Polishable subgroups of $S_{\infty}$

Todor Tsankov (2006)

Fundamenta Mathematicae

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We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group $S_{\infty}$ . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of $S_{\infty}$ . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ...

Plane and layer $(p 2, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

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Closure for spanning trees and distant area

Jun Fujisawa, Akira Saito, Ingo Schiermeyer (2011)

Discussiones Mathematicae Graph Theory

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A k-ended tree is a tree with at most k endvertices. Broersma and Tuinstra [3] have proved that for k ≥ 2 and for a pair of nonadjacent vertices u, v in a graph G of order n with $d e g_{G} u + d e g_{G} v \geq n - 1$ , G has a spanning k-ended tree if and only if G+uv has a spanning k-ended tree. The distant area for u and v is the subgraph induced by the set of vertices that are not adjacent with u or v. We investigate the relationship between the condition on $d e g_{G} u + d e g_{G} v$ and the structure of the distant area for u and v. We prove...

Finite actions on the Klein four-orbifold and prism manifolds

John Kalliongis, Ryo Ohashi (2017)

Commentationes Mathematicae Universitatis Carolinae

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We describe the finite group actions, up to equivalence, which can act on the orbifold $Σ (2, 2, 2)$ , and their quotient types. This is then used to consider actions on prism manifolds $M (b, d)$ which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If $ϕ : G \to Homeo (M (b, d))$ is such an action, we show that $M (b, d) = M (b, 2)$ and $M (b, 2) / ϕ$ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by $Σ (2, 2, 2)$ . For the standard actions, we compute the fundamental group of $M (b, 2) / ϕ$ and...

Displaying similar documents to “Equivalence relations induced by some locally compact groups of homeomorphisms of 2 ℕ ”

Displaying similar documents to “Equivalence relations induced by some locally compact groups of homeomorphisms of $2^{ℕ}$ ”