A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with a convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor implying biautomaticity. As immediate consequences we obtain new results for FC-type Artin groups (in particular braid groups and spherical Artin groups) and weak Garside groups, including e.g. fundamental groups of the complements of complexified finite simplicial arrangements of hyperplanes, braid groups of well-generated complex reflection groups, and one-relator groups with non-trivial center. Among the results are: biautomaticity, existence of EZ and Tits boundaries, the Farrell–Jones conjecture, the coarse Baum–Connes conjecture, and a description of higher order homological and homotopical Dehn functions. As a means of proving the Helly property we introduce and use the notion of a (generalized) cell Helly complex.

如果每个成对相交的组合球族都具有非空交点，则该图为Helly。我们证明了有限型和FC型Artin组的弱Garside组是Helly，即它们在Helly图上具有几何作用。尤其是，这些组在几何上作用于具有凸测地线双梳的空间，从而为它们配备了非正曲率样的结构。该结构具有CAT（0）结构的许多特性，此外，它还具有暗示双自动性的组合风味。作为直接后果，我们获得了FC型Artin组（特别是编织组和球形Artin组）和弱Garside组的新结果，包括例如超平面的复杂有限单调排列的补码的基本组，良好生成的复合体的编织组反思小组 以及具有非平凡中心的单亲小组。结果包括：双自动性，EZ和Tits边界的存在，Farrell-Jones猜想，Baum-Connes粗猜想以及对高阶同构和同位Dehn函数的描述。作为证明Helly属性的一种方法，我们引入并使用了（广义）细胞Helly复合体的概念。