Do you want to publish a course? Click here

Thickness of $mathsf{Out}(A_1*...*A_n)$

92   0   0.0 ( 0 )
 Added by Saikat Das
 Publication date 2018
  fields
and research's language is English
 Authors Saikat Das




Ask ChatGPT about the research

In this paper we have examined hyperbolicity and relative hyperbolicity of $Gamma_n := mathsf{Out}(G_n)$ , where $G_n = A_1*...*A_n$, is a finite free product and each $A_i$ is a finite group. We have used the $mathsf{Out}(G_n)$ action on the Guirardel-Levitt deformation space, to find a virtual generating set and prove quasi isometric embedding of a large class of subgroups. We have used ideas from works of Mosher-Handel and Alibegovic to prove non-distortion. We have used these subgroups to prove that $Gamma_n$ is thick for higher complexities. Thickness was developed by Behrstock-Druc{t}u-Mosher and thickness implies that the groups are non-relatively hyperbolic.



rate research

Read More

S. Gersten announced an algorithm that takes as input two finite sequences $vec K=(K_1,dots, K_N)$ and $vec K=(K_1,dots, K_N)$ of conjugacy classes of finitely generated subgroups of $F_n$ and outputs: (1) $mathsf{YES}$ or $mathsf{NO}$ depending on whether or not there is an element $thetain mathsf{Out}(F_n)$ such that $theta(vec K)=vec K$ together with one such $theta$ if it exists and (2) a finite presentation for the subgroup of $mathsf{Out}(F_n)$ fixing $vec K$. S. Kalajdv{z}ievski published a verification of this algorithm. We present a different algorithm from the point of view of Culler-Vogtmanns Outer space. New results include that the subgroup of $mathsf{Out}(F_n)$ fixing $vec K$ is of type $mathsf{VF}$, an equivariant version of these results, an application, and a unified approach to such questions.
This is the second part of a two part work in which we prove that for every finitely generated subgroup $Gamma < mathsf{Out}(F_n)$, either $Gamma$ is virtually abelian or its second bounded cohomology $H^2_b(Gamma;mathbb{R})$ contains an embedding of $ell^1$. Here in Part II we focus on finite lamination subgroups $Gamma$ --- meaning that the set of all attracting laminations of elements of $Gamma$ is finite --- and on the construction of hyperbolic actions of those subgroups to which the general theory of Part I is applicable.
We prove that $Out(F_N)$ is boundary amenable. This also holds more generally for $Out(G)$, where $G$ is either a toral relatively hyperbolic group or a finitely generated right-angled Artin group. As a consequence, all these groups satisfy the Novikov conjecture on higher signatures.
For any finite collection $f_i$ of fully irreducible automorphisms of the free group $F_n$ we construct a connected $delta$-hyperbolic $Out(F_n)$-complex in which each $f_i$ has positive translation length.
We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $Nge 3$ the number of distinct $Out(F_N)$-conjugacy classes of fully irreducibles $phi$ from an $R$-ball in the Cayley graph of $Out(F_N)$ with $loglambda(phi)$ on the order of $R$ grows exponentially in $R$.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا