CAT(-1) metrics on small cancellation groups

Samuel Brown

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arXiv · 1607.02580

CAT(-1) metrics on small cancellation groups

Samuel Brown

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Abstract

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.

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Samuel Brown. 2016-07-09. CAT(-1) metrics on small cancellation groups. https://arxiv.org/abs/1607.02580

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