## 44 Citations

A Simple Proof of a Theorem of Whyte

- Mathematics
- 2004

Kevin Whyte showed that all Baumslag–Solitar groups BS(p,q) with 1 < p < q are quasi-isometric [Whyte, K., Geom. Funct. Anal. 11 (2001), 1327–1343]. We provide an elementary geometric proof.

Quasi-actions on trees I. Bounded valence

- Mathematics
- 2000

Given a bounded valence, bushy tree T, we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T'. This theorem has many…

Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II

- Mathematics
- 1998

Let BS(1,n)= . We prove that any finitely-generated group quasi-isometric to BS(1,n) is (up to finite groups) isomorphic to BS(1,n). We also show that any uniform group of quasisimilarities of the…

Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem

- Mathematics
- 2013

In this paper, we study the question of classifying self-similar sets under bi-Lipschitz mappings and obtain an important bi-Lipschitz invariant, which is an ideal of a ring related to IFS. Roughly…

Problems on the geometry of finitely generated solvable groups

- Mathematics
- 2000

A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.

Morse quasiflats I

- Mathematics, Computer ScienceJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2022

This paper introduces a number of alternative definitions of Morse quasiflats, and under appropriate assumptions on the ambient space it is shown that they are equivalent and quasi-isometry invariant; it also gives a variety of examples.

Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2021

Abstract We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let G be a…

Twisted conjugacy and commensurability invariance

- MathematicsJournal of Group Theory
- 2021

Abstract A group 𝐺 is said to have property R ∞ R_{\infty} if, for every automorphism φ ∈ Aut ( G ) \varphi\in\mathrm{Aut}(G) , the cardinality of the set of 𝜑-twisted conjugacy classes is…

The geometry of groups containing almost normal subgroups

- MathematicsGeometry & Topology
- 2021

A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ is commensurable to $H$. If $H$ is almost normal, there is a well-defined quotient space $G/H$. We show that if a group $G$…

## References

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Measure theory and fine properties of functions

- Mathematics
- 1992

GENERAL MEASURE THEORY Measures and Measurable Functions Lusin's and Egoroff's Theorems Integrals and Limit Theorems Product Measures, Fubini's Theorem, Lebesgue Measure Covering Theorems…

Quasi-flats and rigidity in higher rank symmetric spaces

- Mathematics
- 1997

In this paper we use elementary geometrical and topological methods to study some questions about the coarse geometry of symmetric spaces. Our results are powerful enough to apply to noncocompact…

A note on centrality in 3-manifold groups

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1990

Centralizers in fundamental groups of 3-manifolds are well understood because of their relationship with Seifert fibre spaces. Jaco and Shalen's book [4] provides detailed information about Seifert…

Seifert fibered spaces in 3-manifolds

- Mathematics
- 1979

Publisher Summary This chapter describes Seifert Fibered Spaces in 3-Manifolds. There exist finitely many disjoint, non-contractible, pairwise non-parallel, embedded 2-spheres in M, whose homotopy…

The quasi-isometry classification of rank one lattices

- Mathematics
- 1995

Let X be a symmetric space—other than the hyperbolic plane—of strictly negative sectional curvature. Let G be the isometry group of X. We show that any quasi-isometry between non-uniform lattices in…

The quasi-isometry classification of lattices in semisimple Lie groups

- Mathematics
- 1997

This paper is a report on the recently completed quasi-isometry classification of lattices in semisimple 1 Lie groups. The main theorems stated here are a summary of work of several people over a…