Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the topological dimension of the Gromov boundaries of some hyperbolic $Out(F_N)$-graphs
237
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a finitely generated free group.
rate research
Read More
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 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.
We study quasi-isometry invariants of Gromov hyperbolic spaces, focussing on the l_p-cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous l_p-cohomology, thereby obtaining information about the l_p-equivalence relation, as well as critical exponents associated with l_p-cohomology. As an application, we provide a flexible construction of hyperbolic groups which do not have the Combinatorial Loewner Property, extending and complementing earlier examples. Another consequence is the existence of hyperbolic groups with Sierpinski carpet boundary which have conformal dimension arbitrarily close to 1. In particular, we answer questions of Mario Bonk and John Mackay.
We show that in large enough rank, the Gromov boundary of the free factor complex is path connected and locally path connected.
$Out(F_n):=Aut(F_n)/Inn(F_n)$ denotes the outer automorphism group of the rank $n$ free group $F_n$. An element $phi$ of $Out(F_n)$ is polynomially growing if the word lengths of conjugacy classes in $F_n$ grow at most polynomially under iteration by $phi$. We restrict attention to the subset $UPG(F_n)$ of $Out(F_n)$ consisting of polynomially growing elements whose action on $H_1(F_n, Z)$ is unipotent. In particular, if $phi$ is polynomially growing and acts trivially on $H_1(F_n,Z_3)$ then $phi$ is in $UPG(F_n)$ and also every polynomially growing element of $Out(F_n)$ has a positive power that is in $UPG(F_n)$. In this paper we solve the conjugacy problem for $UPG(F_n)$. Specifically we construct an algorithm that takes as input $phi, psiin UPG(F_n)$ and outputs YES or NO depending on whether or not there is $thetain Out(F_n)$ such that $psi=thetaphitheta^{-1}$. Further, if YES then such a $theta$ is produced.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
