论文标题
$ {\ rm cat（0）} $ Cube Complexs的触点图的自动形态
Automorphisms of contact graphs of ${\rm CAT(0)}$ cube complexes
论文作者
论文摘要
我们表明，在薄弱的假设下，$ {\ rm cat（0）} $ cube complex $ x $与Hagen's Contact Graph $ \ MATHCAL {C C}（C}（X）$相吻合的自动形态组。结果尤其是对于萨尔维蒂复合物的通用覆盖物，它提供了伊万诺夫定理在非孢子表面的曲线图上的类似物。这突出了触点图和Kim-Koberda扩展图之间的对比度，它们具有更大的自动形态组。我们还研究了与右角高级甲基组的戴维斯复合物相关的接触图。我们表明，这些接触图的行为较不那么良好，并与戴维斯综合体的普遍掩护相比，准确地描述了它们何时具有更多的自动形态。
We show that, under weak assumptions, the automorphism group of a ${\rm CAT(0)}$ cube complex $X$ coincides with the automorphism group of Hagen's contact graph $\mathcal{C}(X)$. The result holds, in particular, for universal covers of Salvetti complexes, where it provides an analogue of Ivanov's theorem on curve graphs of non-sporadic surfaces. This highlights a contrast between contact graphs and Kim-Koberda extension graphs, which have much larger automorphism group. We also study contact graphs associated to Davis complexes of right-angled Coxeter groups. We show that these contact graphs are less well-behaved and describe exactly when they have more automorphisms than the universal cover of the Davis complex.
