{"id":"openai-math/A-hyperbolic-group-with-no-geometric-CAT0-action","pdf":"https://github.com/openai/math/blob/main/preprints/A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-hyperbolic-group-with-no-geometric-CAT0-action-September-25-2026","tags":["geometric-group-theory","cat0-geometry","hyperbolic-groups"],"score":0,"title":"A hyperbolic group with no geometric CAT(0) action","domain":"Group theory","family":"257","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We construct a hyperbolic group with a finite classifying space that admits no geometric action on a proper complete CAT(0) space. Consequently, a finite aspherical simplicial complex with a linear combinatorial disk-filling inequality need not have a finite locally CAT(0) homotopy model, and hence need not have a finite locally CAT(−1) model. Here metric models carry geodesic length metrics inducing the given complex topology.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"A hyperbolic group without a geometric CAT(0) action"}