# Simplicial nonpositive curvature

Tadeusz Januszkiewicz; Jacek Świątkowski

Publications Mathématiques de l'IHÉS (2006)

- Volume: 104, page 1-85
- ISSN: 0073-8301

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topJanuszkiewicz, Tadeusz, and Świątkowski, Jacek. "Simplicial nonpositive curvature." Publications Mathématiques de l'IHÉS 104 (2006): 1-85. <http://eudml.org/doc/104219>.

@article{Januszkiewicz2006,

abstract = {We introduce a family of conditions on a simplicial complex that we call local k-largeness (k≥6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the non-positive curvature: locally 6-large spaces have many properties similar to non-positively curved ones. However, local 6-largeness neither implies nor is implied by non-positive curvature of the standard metric. One can think of these results as a higher dimensional version of small cancellation theory. On the other hand, we show that k-largeness implies non-positive curvature if k is sufficiently large. We also show that locally k-large spaces exist in every dimension. We use this to answer questions raised by D. Burago, M. Gromov and I. Leary.},

author = {Januszkiewicz, Tadeusz, Świątkowski, Jacek},

journal = {Publications Mathématiques de l'IHÉS},

keywords = {simplicial complex; -largeness; piecewise euclidean metric; CAT(0) property; Gromov hyperbolicity},

language = {eng},

pages = {1-85},

publisher = {Springer},

title = {Simplicial nonpositive curvature},

url = {http://eudml.org/doc/104219},

volume = {104},

year = {2006},

}

TY - JOUR

AU - Januszkiewicz, Tadeusz

AU - Świątkowski, Jacek

TI - Simplicial nonpositive curvature

JO - Publications Mathématiques de l'IHÉS

PY - 2006

PB - Springer

VL - 104

SP - 1

EP - 85

AB - We introduce a family of conditions on a simplicial complex that we call local k-largeness (k≥6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the non-positive curvature: locally 6-large spaces have many properties similar to non-positively curved ones. However, local 6-largeness neither implies nor is implied by non-positive curvature of the standard metric. One can think of these results as a higher dimensional version of small cancellation theory. On the other hand, we show that k-largeness implies non-positive curvature if k is sufficiently large. We also show that locally k-large spaces exist in every dimension. We use this to answer questions raised by D. Burago, M. Gromov and I. Leary.

LA - eng

KW - simplicial complex; -largeness; piecewise euclidean metric; CAT(0) property; Gromov hyperbolicity

UR - http://eudml.org/doc/104219

ER -

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