A rigidity theorem for the solvable Baumslag-Solitar groups

@article{Farb1998ART,
  title={A rigidity theorem for the solvable Baumslag-Solitar groups},
  author={Benson Farb and Lee Mosher},
  journal={Inventiones mathematicae},
  year={1998},
  volume={131},
  pages={419-451}
}
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36 Citations
Highly Influential Citations
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Methods Citations
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36 Citations

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References

SHOWING 1-10 OF 13 REFERENCES

The large-scale geometry of Hilbert modular groups

Measure theory and fine properties of functions

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

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

  • P. Kropholler
  • Mathematics
    Mathematical 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…

Quasi-isometric rigidity and diophantine approximation

Seifert fibered spaces in 3-manifolds

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…

Asymptotic invariants of infinite groups

The quasi-isometry classification of rank one lattices

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

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…

On the shape of Cantor sets