We prove that every action of a group on a link collapsible simplicial complex fixes a simplex. Under additional assumptions, the set of points fixed by the action induced on the geometric realization of the complex is contractible. In particular, it follows that the set of fixed points of the geometric realization of a simplicial endomorphism of a link collapsible clique complex is contractible and that the evasiveness conjecture holds for link-collapsible simplicial complexes.

中文翻译：

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链接可折叠单纯复形上群动作的固定点

我们证明了一个群在链接可折叠单纯复形上的每一个动作都会修复一个单纯形。在额外的假设下，由复合体的几何实现引起的动作固定的点集是可收缩的。特别是，可推导出链接可折叠团复形的单纯自同态的几何实现的不动点集是可收缩的，并且回避猜想适用于链接可折叠单纯复形。