雷顿定理:扩展、极限和拟树

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2020-09-09 DOI:10.2140/agt.2022.22.881

M. Bridson, Sam Shepherd

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引用次数: 2

摘要

雷顿定理指出，如果有一棵树$T$覆盖了两个有限图$G_1$和$G_2$，那么就有一个有限图$G $被$T$覆盖并且同时覆盖了$G_1$和$G_2$。我们证明了这个结果不能推广到除树以外的图的正则覆盖上。即使拟树的自同构群包含一致格，它也不能推广到拟树的非正则覆盖。但它确实延伸到准树的规则覆盖物。

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Leighton’s theorem : Extensions, limitations and quasitrees

Leighton's Theorem states that if there is a tree $T$ that covers two finite graphs $G_1$ and $G_2$, then there is a finite graph $\hat G$ that is covered by $T$ and covers both $G_1$ and $G_2$. We prove that this result does not extend to regular covers by graphs other than trees. Nor does it extend to non-regular covers by a quasitree, even if the automorphism group of the quasitree contains a uniform lattice. But it does extend to regular coverings by quasitrees.

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