There is a finite connected aspherical complex with a linear combinatorial disk-filling bound whose word-hyperbolic fundamental group has no proper cocompact isometric action on any nonempty proper complete CAT(0) space.
There is a finite connected aspherical complex with a linear combinatorial disk-filling bound whose word-hyperbolic fundamental group has no proper cocompact isometric action on any nonempty proper complete CAT(0) space.
There is a finite connected aspherical complex with a linear combinatorial disk-filling bound whose word-hyperbolic fundamental group has no proper cocompact isometric action on any nonempty proper complete CAT(0) space.
If correct, gives a dimension-independent obstruction to geometric CAT(0) realization of a hyperbolic group.
Must every word-hyperbolic group admit a geometric action on a proper CAT(0) space?
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OpenAI reports a hyperbolic group without a geometric CAT(0) action
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