### Abstract

Original language | English |
---|---|

Pages (from-to) | 125-140 |

Number of pages | 16 |

Journal | Geometriae Dedicata |

Volume | 55 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Apr 1995 |

### Cite this

*Geometriae Dedicata*,

*55*(2), 125-140. https://doi.org/10.1007/BF01264925

**Almost convex groups and the eight geometries.** / Shapiro, Michael; Stein, Melanie.

Research output: Contribution to journal › Article

*Geometriae Dedicata*, vol. 55, no. 2, pp. 125-140. https://doi.org/10.1007/BF01264925

}

TY - JOUR

T1 - Almost convex groups and the eight geometries

AU - Shapiro, Michael

AU - Stein, Melanie

PY - 1995/4/1

Y1 - 1995/4/1

N2 - IfM is a closed Nil geometry 3-manifold then π1(M) is almost convex with respect to a fairly simple “geometric” generating set. IfG is a central extension or a ℤ extension of a word hyperbolic group, thenG is also almost convex with respect to some generating set. Combining these with previously known results shows that ifM is a closed 3-manifold with one of Thurston's eight geometries, π1(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol.

AB - IfM is a closed Nil geometry 3-manifold then π1(M) is almost convex with respect to a fairly simple “geometric” generating set. IfG is a central extension or a ℤ extension of a word hyperbolic group, thenG is also almost convex with respect to some generating set. Combining these with previously known results shows that ifM is a closed 3-manifold with one of Thurston's eight geometries, π1(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol.

U2 - 10.1007/BF01264925

DO - 10.1007/BF01264925

M3 - Article

VL - 55

SP - 125

EP - 140

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 2

ER -