$Z_n$-actions on 3-manifolds

Józef H. Przytycki

Displaying similar documents to “ $Z_{n}$ -actions on 3-manifolds”

Cyclic actions on $S^{2}$ - and $P^{2}$ -bundles over $S^{1}$

Józef H. Przytycki (1982)

Colloquium Mathematicae

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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...

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.

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...

Actions of $Z_{n}$ on some surface-bundles over $S^{1}$

Józef H. Przytycki (1982)

Colloquium Mathematicae

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A ratio ergodic theorem for multiparameter non-singular actions

Michael Hochman (2010)

Journal of the European Mathematical Society

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We prove a ratio ergodic theorem for non-singular free $ℤ^{d}$ and $ℝ^{d}$ actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in $ℝ^{d}$ . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general...

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.

Correction for the paper “ $S^{3}$ -bundles and exotic actions”

T. E. Barros (2001)

Bulletin de la Société Mathématique de France

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In [R] explicit representatives for $S^{3}$ -principal bundles over $S^{7}$ are constructed, based on these constructions explicit free $S^{3}$ -actions on the total spaces are described, with quotients exotic $7$ -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic $7$ -spheres that occur as quotients of the free $S^{3}$ -actions described...

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

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The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the $n$ -dimensional torus, its identity component is a simple group. For $U (1)$ fibered manifolds, for manifolds admitting special semi-free $U (1)$ actions and for 2- or 3-dimensional manifolds with nontrivial $U (1)$ actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

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 $W$ .

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.

$Z ₂^{k}$ -actions fixing point ∪ Vⁿ

Pedro L. Q. Pergher (2002)

Fundamenta Mathematicae

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We describe the equivariant cobordism classification of smooth actions $(M^{m}, Φ)$ of the group $G = Z ₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally,...

$Z ₂^{k}$ -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

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Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if $N^{m}$ is any smooth and closed m-dimensional manifold with m > n and $T : N^{m} \to N^{m}$ is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions $(M^{m}; Φ)$ of the group $G = Z ₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček (1999)

Discussiones Mathematicae Graph Theory

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So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_{d}$ of a given dimension d was $K_{d 2^{d - 1}, d 2^{d - 2}}$ . We improve this result and show that also $K_{d 2^{d - 2}, d 2^{d - 2}}$ allows a cyclic decomposition into $Q_{d}$ . We also present a cyclic factorization of $K_{8, 8}$ into Q₄.

Real algebraic actions on projective spaces - A survey

Ted Petrie (1973)

Annales de l'institut Fourier

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Let $G$ be a compact lie group. We introduce the set $S_{G} (Y)$ for every smooth $G$ manifold $Y$ . It consists of equivalence classes of pair $(X, f)$ where $f : X \to Y$ is a $G$ map which defines a homotopy equivalence from $X$ to $Y$ . Two pairs $(X_{i}, f_{i})$ , for $i = 0, 1$ , are equivalent if there is a $G$ homotopy equivalence $φ : X_{0} \to X_{1}$ such that $f_{0}$ is $G$ homotopic to $f_{1} \circ φ$ . Properties of the set $S_{G} (Y)$ and related to the representation of $G$ on the tangent spaces of $X$ and $Y$ at the fixed points. For the case $G = S^{1}$ and $Y$ is the $S^{1}$ manifold defined by a “linear”...

Explicit computations of all finite index bimodules for a family of II $_{1}$ factors

Stefaan Vaes (2008)

Annales scientifiques de l'École Normale Supérieure

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We study II $_{1}$ factors $M$ and $N$ associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index $M$ - $N$ -bimodule (in particular, every isomorphism between $M$ and $N$ ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index $M$ - $M$ -bimodules is identified with an extended Hecke fusion algebra,...

Displaying similar documents to “ Z n -actions on 3-manifolds”

Displaying similar documents to “ $Z_{n}$ -actions on 3-manifolds”