### Abstract

We determine the structure of finitely generated groups which are quasi-isometric to nonpositively curved symmetric spaces, allowing Euclidean de Rham factors. If X is a symmetric space of noncompact type (i.e. it has no Euclidean de Rham factor), and Γ is a finitely generated group quasi-isometric to the product double-struck E sign^{k} x X, then there is an exact sequence 1 → H → Γ → L → 1 where H . contains a finite index copy of ℤ^{k} and L is a uniform lattice in the isometry group of X.

Original language | English (US) |
---|---|

Pages (from-to) | 239-260 |

Number of pages | 22 |

Journal | Communications in Analysis and Geometry |

Volume | 9 |

Issue number | 2 |

State | Published - Apr 2001 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Geometry and Topology

### Cite this

*Communications in Analysis and Geometry*,

*9*(2), 239-260.

**Groups quasi-isometric to symmetric spaces.** / Kleiner, Bruce; Leeb, Bernhard.

Research output: Contribution to journal › Article

*Communications in Analysis and Geometry*, vol. 9, no. 2, pp. 239-260.

}

TY - JOUR

T1 - Groups quasi-isometric to symmetric spaces

AU - Kleiner, Bruce

AU - Leeb, Bernhard

PY - 2001/4

Y1 - 2001/4

N2 - We determine the structure of finitely generated groups which are quasi-isometric to nonpositively curved symmetric spaces, allowing Euclidean de Rham factors. If X is a symmetric space of noncompact type (i.e. it has no Euclidean de Rham factor), and Γ is a finitely generated group quasi-isometric to the product double-struck E signk x X, then there is an exact sequence 1 → H → Γ → L → 1 where H . contains a finite index copy of ℤk and L is a uniform lattice in the isometry group of X.

AB - We determine the structure of finitely generated groups which are quasi-isometric to nonpositively curved symmetric spaces, allowing Euclidean de Rham factors. If X is a symmetric space of noncompact type (i.e. it has no Euclidean de Rham factor), and Γ is a finitely generated group quasi-isometric to the product double-struck E signk x X, then there is an exact sequence 1 → H → Γ → L → 1 where H . contains a finite index copy of ℤk and L is a uniform lattice in the isometry group of X.

UR - http://www.scopus.com/inward/record.url?scp=25644450400&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25644450400&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 239

EP - 260

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 2

ER -