اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn closed subgroups of the group of homeomorphisms of a manifold
293
0
0.0
(
0
)
تأليف
Frederic Le Roux
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of $homeo_{0}(M)$ (the identity component of the group of homeomorphisms of $M$), the subgroup consisting of volume preserving elements is maximal.
قيم البحث
اقرأ أيضاً
We prove that Thompsons group $F$ has a subgroup $H$ such that the conjugacy problem in $H$ is undecidable and the membership problem in $H$ is easily decidable. The subgroup $H$ of $F$ is a closed subgroup of $F$. That is, every function in $F$ whic
h is a piecewise-$H$ function belongs to $H$. Other interesting examples of closed subgroups of $F$ include Jones subgroups $overrightarrow{F}_n$ and Jones $3$-colorable subgroup $mathcal F$. By a recent result of the first author, all maximal subgroups of $F$ of infinite index are closed. In this paper we prove that if $Kleq F$ is finitely generated then the closure of $K$, i.e., the smallest closed subgroup of $F$ which contains $K$, is finitely generated. We also prove that all finitely generated closed subgroups of $F$ are undistorted in $F$. In particular, all finitely generated maximal subgroups of $F$ are undistorted in $F$.
We define kinetic Brownian motion on the diffeomorphism group of a closed Riemannian manifold, and prove that it provides an interpolation between the hydrodynamic flow of a fluid and a Brownian-like flow.
We generalize the hamiltonian topology on hamiltonian isotopies to an intrinsic symplectic topology on the space of symplectic isotopies. We use it to define the group $SSympeo(M,omega)$ of strong symplectic homeomorphisms, which generalizes the grou
p $Hameo(M,omega)$ of hamiltonian homeomorphisms introduced by Oh and Muller. The group $SSympeo(M,omega)$ is arcwise connected, is contained in the identity component of $Sympeo(M,omega)$; it contains $Hameo(M,omega)$ as a normal subgroup and coincides with it when $M$ is simply connected. Finally its commutator subgroup $[SSympeo(M,omega),SSympeo(M,omega)]$ is contained in $Hameo(M,omega)$.
In 1980, Albert Fathi asked whether the group of area-preserving homeomorphisms of the 2-disc that are the identity near the boundary is a simple group. In this paper, we show that the simplicity of this group is equivalent to the following fragmenta
tion property in the group of compactly supported, area preserving diffeomorphisms of the plane: there exists a constant m such that every element supported on a disc D is the product of at most m elements supported on topological discs whose area are half the area of D.
We study the polynomial entropy of the wandering part of any invertible dynamical system on a compact metric space. As an application we compute the polynomial entropy of Brouwer homeomorphisms (fixed point free orientation preserving homeomorphisms
of the plane), and show in particular that it takes every real value greater or equal to 2.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
