We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3‐Calabi–Yau triangulated category. The motivation/application is that the result will be used to show that the (principal component of) space of stability conditions on the 3‐Calabi–Yau category is simply connected in the sequel [King and Qiu, Invent. Math., to appear].

中文翻译：

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装饰性标记表面的球形/编织扭曲组的有限展示

我们对装饰表面的编织扭曲组给出了有限的表示。如果装饰表面来自三角形的标记表面而没有刺孔，我们将获得相关的3-Calabi–Yau三角分类类别的球形扭曲组的有限表示。动机/应用是，该结果将用于显示在3-Calabi–Yau类别上，稳定性条件的（主要组成部分）空间在续集中简单地关联了[King and Qiu，Invent。数学。，出现]。