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arXiv · 1305.4661

A combinatorial non-positive curvature I: weak systolicity

Damian Osajda
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Abstract

We introduce the notion of weakly systolic complexes and groups, and initiate regular studies of them. Those are simplicial complexes with nonpositive-curvature-like properties and groups acting on them geometrically. We characterize weakly systolic complexes as simply connected simplicial complexes satisfying some local combinatorial conditions. We provide several classes of examples --- in particular systolic groups and CAT(-1) cubical groups are weakly systolic. We present applications of the theory, concerning Gromov hyperbolic groups, Coxeter groups and systolic groups.

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Damian Osajda. 2013-05-20. A combinatorial non-positive curvature I: weak systolicity. https://arxiv.org/abs/1305.4661

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