Simplicial nonpositive curvature
Januszkiewicz, Tadeusz ; Świątkowski, Jacek
Publications Mathématiques de l'IHÉS, Tome 104 (2006), p. 1-85 / Harvested from Numdam
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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.

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     author = {Januszkiewicz, Tadeusz and \'Swi\k atkowski, Jacek},
     title = {Simplicial nonpositive curvature},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {104},
     year = {2006},
     pages = {1-85},
     doi = {10.1007/s10240-006-0038-5},
     mrnumber = {2264834},
     zbl = {pre05117094},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_2006__104__1_0}
}

Januszkiewicz, Tadeusz; Świątkowski, Jacek. Simplicial nonpositive curvature. Publications Mathématiques de l'IHÉS, Tome 104 (2006) pp. 1-85. doi : 10.1007/s10240-006-0038-5. http://gdmltest.u-ga.fr/item/PMIHES_2006__104__1_0/

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