Simplicial nonpositive curvature

  • Tadeusz JanuszkiewiczEmail author
  • Jacek ŚwiątkowskiEmail author


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.


Simplicial Complex Local Group Nonpositive Curvature Injective Morphism Deformation Retract 
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© Institut des Hautes Études Scientifiques and Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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