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Barely CAT(-1) groups are acylindrically hyperbolic. (arXiv:1712.04736v1 [math.GR])
来源于:arXiv
In this paper, we show that, if a group $G$ acts geometrically on a
geodesically complete CAT(0) space $X$ which contains at least one point with a
CAT(-1) neighborhood, then $G$ must be either virtually cyclic or
acylindrically hyperbolic. As a consequence, the fundamental group of a compact
Riemannian manifold whose sectional curvature is nonpositive everywhere and
negative in at least one point is either virtually cyclic or acylindrically
hyperbolic. This statement provides a precise interpretation of an idea
expressed by Gromov in his paper Asymptotic invariants of infinite groups. 查看全文>>