### Abstract

Let S be a smooth 3-dimensional nonpositively curved Riemannian manifold with corners, whose boundary consists of a finite number of geodesically convex nonpositively curved faces (for example, a Euclidean or hyperbolic polyhedron). We show that it is always possible to glue together finitely many copies of S so as to get a nonpositively curved pseudomanifold without boundary.

Original language | English (US) |
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Pages (from-to) | 1493-1498 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 129 |

Issue number | 5 |

State | Published - Dec 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*129*(5), 1493-1498.

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*Proceedings of the American Mathematical Society*, vol. 129, no. 5, pp. 1493-1498.

**Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseud omanifold.** / Burago, Dmitri; Ferleger, S.; Kleiner, B.; Kononenko, A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseud omanifold

AU - Burago, Dmitri

AU - Ferleger, S.

AU - Kleiner, B.

AU - Kononenko, A.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - Let S be a smooth 3-dimensional nonpositively curved Riemannian manifold with corners, whose boundary consists of a finite number of geodesically convex nonpositively curved faces (for example, a Euclidean or hyperbolic polyhedron). We show that it is always possible to glue together finitely many copies of S so as to get a nonpositively curved pseudomanifold without boundary.

AB - Let S be a smooth 3-dimensional nonpositively curved Riemannian manifold with corners, whose boundary consists of a finite number of geodesically convex nonpositively curved faces (for example, a Euclidean or hyperbolic polyhedron). We show that it is always possible to glue together finitely many copies of S so as to get a nonpositively curved pseudomanifold without boundary.

UR - http://www.scopus.com/inward/record.url?scp=23044527782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044527782&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044527782

VL - 129

SP - 1493

EP - 1498

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -