In this paper, we initiate a geometric study of graph braid groups. More precisely, by applying the formalism of special colorings introduced in a previous paper, we determine precisely when a graph braid group is Gromov-hyperbolic, toral relatively hyperbolic and acylindrically hyperbolic.

中文翻译：

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图编织组中的负曲率

在本文中，我们启动了图形编织组的几何研究。更准确地说，通过应用前一篇论文中介绍的特殊着色的形式，我们精确地确定了图编织群何时是格罗莫夫双曲线、环相对双曲线和非圆柱双曲线。