2016/07/09 by Samuel Brown, Brown, Samuel
Mathematics · #20F65 #20F67 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1607.02580
openalex publication_date 2016/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a proof that groups satisfying the "uniform C'(1/6)" small cancellation condition admit a geometric action on a CAT(-1) space. It follows that random groups at density <1/12 are CAT(-1). The proof consists of a direct construction of a piecewise hyperbolic structure on the presentation complex of such a group, together with folding moves to make the complex negatively curved. The argument was originally suggested by Gromov.