Continuously many quasiisometry classes of 2-generator groups

  title={Continuously many quasiisometry classes of 2-generator groups},
  author={Brian H. Bowditch},
  journal={Commentarii Mathematici Helvetici},
  • B. Bowditch
  • Published 30 June 1998
  • Mathematics
  • Commentarii Mathematici Helvetici
Abstract. We construct continuously many quasiisometry classes of torsion-free 2-generator small cancellation groups.  
Continuously Many Quasi-isometry Classes of Residually Finite Groups
. We study a family of finitely generated residually finite small cancellation groups. These groups are quotients of F 2 depending on a subset S of positive integers. Varying S yields continuously many
On the complexity of the quasi-isometry and virtual isomorphism problems for finitely generated groups
We study the Borel complexity of the quasi-isometry and virtual isomorphism problems for the class of finitely generated groups.
Asymptotic Cones of Finitely Generated Groups
Answering a question of Gromov [7], we shall present an example of a finitely generated group Γ and two non‐principal ultrafilters A, B such that the asymptotic cones ConA Γ and ConB Γ are not
Cayley graphs of finitely generated groups
There does not exist a Borel choice of generators for each finitely generated group which has the property that isomorphic groups are assigned isomorphic Cayley graphs.
Infinitely presented C(6)‐groups are SQ‐universal
It is proved that infinitely presented classical C(6) small cancellation groups are SQ-universal and the result is extended to graphical $Gr_*( 6)$-groups over free products.
Constructing groups of type $FP_2$ over fields but not over the integers
We construct examples of groups that are FP2(Q) and FP2(Z/pZ) for all primes p but not of type FP2(Z).
Infinitely presented graphical small cancellation groups are acylindrically hyperbolic
We prove that infinitely presented graphical Gr(7) small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical C(7)-groups and, hence, classical C′( 1 6
Dehn function and asymptotic cones of Abels’ group
We prove that Abels’ group over an arbitrary non‐discrete locally compact field has a quadratic Dehn function. As applications, we exhibit connected Lie groups and polycyclic groups whose asymptotic
Uncountably many quasi-isometry classes of groups of type FP
Abstract:In an earlier paper, one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincar\\'e duality groups for each $n\\geq 4$. We show that those
The geometry of generalized loxodromic elements
We explore geometric conditions which ensure a given element of a finitely generated group is, or fails to be, generalized loxodromic; as part of this we prove a generalization of Sisto's result that


Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means
This paper gives a negative solution to the problem of Milnor concerning the degrees of growth of groups. The construction also answers a question of Day concerning amenable groups. A number of other
Combinatorial Group Theory
Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.
Gromov , Asymptotic invariants of infinite groups
  • Izv . Acad . Nauk SSSR , Ser . Mat .
  • 1984