# Continuously many quasiisometry classes of 2-generator groups

@article{Bowditch1998ContinuouslyMQ, title={Continuously many quasiisometry classes of 2-generator groups}, author={Brian H. Bowditch}, journal={Commentarii Mathematici Helvetici}, year={1998}, volume={73}, pages={232-236} }

Abstract. We construct continuously many quasiisometry classes of torsion-free 2-generator small cancellation groups.

## 24 Citations

Continuously Many Quasi-isometry Classes of Residually Finite Groups

- Mathematics
- 2022

. 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

- Mathematics
- 2008

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

- Mathematics
- 2000

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

- Mathematics
- 2005

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

- MathematicsJ. Lond. Math. Soc.
- 2015

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

- Mathematics
- 2021

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

- Mathematics
- 2014

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

- Mathematics
- 2013

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

- MathematicsAmerican Journal of Mathematics
- 2020

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

- Mathematics
- 2018

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…

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