Foliations by planes and Lie group actions

J. A. Álvarez López; J. L. Arraut; C. Biasi

The search session has expired. Please query the service again.

Displaying similar documents to “Foliations by planes and Lie group actions”

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

Similarity:

It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_{G}$ . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^{r}$ diffeomorphism group G is simple iff the foliation $ℱ_{[G, G]}$ defined by [G,G] admits no proper...

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

Similarity:

The notion of the Hausdorffized leaf space $\tilde{}$ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to $\tilde{}$ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to $\tilde{}$ is shown. Finally, some examples are examined.

Finite actions on the Klein four-orbifold and prism manifolds

John Kalliongis, Ryo Ohashi (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Real algebraic actions on projective spaces - A survey

Ted Petrie (1973)

Annales de l'institut Fourier

Similarity:

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”...

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

T. E. Barros (2001)

Bulletin de la Société Mathématique de France

Similarity:

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...

Groups of $C^{r, s}$ -diffeomorphisms related to a foliation

Jacek Lech, Tomasz Rybicki (2007)

Banach Center Publications

Similarity:

The notion of a $C^{r, s}$ -diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of $C^{r, s}$ -diffeomorphisms is proved. A remark on $C^{n + 1}$ -diffeomorphisms is given.

Minimal, rigid foliations by curves on $ℂ ℙ^{n}$

Frank Loray, Julio C. Rebelo (2003)

Journal of the European Mathematical Society

Similarity:

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space $ℂ ℙ^{n}$ for every dimension $n \geq 2$ and every degree $d \geq 2$ . Precisely, we construct a foliation $ℱ$ which is induced by a homogeneous vector field of degree $d$ , has a finite singular set and all the regular leaves are dense in the whole of $ℂ ℙ^{n}$ . Moreover, $ℱ$ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if $ℱ$ is conjugate to another holomorphic...

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

Bruno P. Zimmermann (2014)

Fundamenta Mathematicae

Similarity:

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...

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

Jarosław Kwapisz (2010)

Fundamenta Mathematicae

Similarity:

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.

Shadowing in multi-dimensional shift spaces

Piotr Oprocha (2008)

Colloquium Mathematicae

Similarity:

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.

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

Adrian Ioana (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

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 ${SL}_{2} (ℤ)$ .

$Z ₂^{k}$ -actions fixing point ∪ Vⁿ

Pedro L. Q. Pergher (2002)

Fundamenta Mathematicae

Similarity:

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,...

Shadowing in actions of some Abelian groups

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

Fundamenta Mathematicae

Similarity:

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.

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

Marcos Craizer (1994)

Annales de l'institut Fourier

Similarity:

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 $W$ .

Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska (2001)

Fundamenta Mathematicae

Similarity:

Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space $(B_{p} (G)) / G$ of the classifying space of the category associated to the G-poset $_{p} (G)$ of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor $X^{E ₙ} / (N E ₀ \cap . . . \cap N E ₙ)$ defined over the poset $(s d_{p} (G)) / G$ , where sd is the barycentric subdivision....

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

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.

Torus embeddings, polyhedra, k*-actions and homology

Jerzy Jurkiewicz

Similarity:

CONTENTSIntroduction..............................................................................................51. General torus embeddings...................................................................7 1.1. Sets of subrings..............................................................................7 1.2. Complex of cones and torus embeddings. Basic properties and notation...............8 1.3. Jets of 1-p.s. at 0...........................................................................12 1.4....

Foliations by complex manifolds involving the complex Hessian

Julian Ławrynowicz, Jerzy Kalina, Masami Okada

Similarity:

SummaryIn 1979 the second named author proved, in a joint paper with J. Ławrynowicz, the existence of a foliation of a bounded domain in $ℂ^{n}$ by complex submanifolds of codimension k+p-1, connected in some sense with a real (1,1) C³-form of rank k and the pth power of the complex Hessian of a C³-function u with im u plurisubharmonic and the property that for every leaf of this foliation the restricted functions im u, re u and $(\partial / \partial z_{j}) i m u$ , $(\partial / \partial z_{j}) r e u$ are pluriharmonic and holomorphic, respectively.Now the...

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

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

Fundamenta Mathematicae

Similarity:

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....

G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

Similarity:

We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map $h o c o l i m_{_{d}} G / d (-) \to | W |$ which is a (non-equivariant) homotopy equivalence, hence $h o c o l i m_{_{d}} E G \times_{G} F_{d} \to E G \times_{G} | W |$ is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy...

A note on singular homology groups of infinite products of compacta

Kazuhiro Kawamura (2002)

Fundamenta Mathematicae

Similarity:

Let n be an integer with n ≥ 2 and $X_{i}$ be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of $Σ (\prod_{i} X_{i})$ with those of $\prod_{i} Σ X_{i}$ (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.