ε-agreement is solvable in every CUB space, and simplex agreement on a simplicial complex C is solvable for n+1 processes iff C is (n-1)-connected.
A combinatorial non-positive curvature I: weak systolicity
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
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.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
Groups with navigable path systems satisfy weak rank rigidity and the Morse local-to-global property, proved uniformly via a new generalised contraction space.
Geodesic halfspace separation is polynomial-time solvable on weakly bridged graphs, pseudo-modular graphs, and matroid basis graphs.
citing papers explorer
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Solving Approximate Agreement on continuous and discrete spaces
ε-agreement is solvable in every CUB space, and simplex agreement on a simplicial complex C is solvable for n+1 processes iff C is (n-1)-connected.
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Weak rank rigidity for groups with a navigable path system
Groups with navigable path systems satisfy weak rank rigidity and the Morse local-to-global property, proved uniformly via a new generalised contraction space.
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Halfspace separation in geodesic convexity
Geodesic halfspace separation is polynomial-time solvable on weakly bridged graphs, pseudo-modular graphs, and matroid basis graphs.