2-chains and square roots of Thompson’s group
2-chains and square roots of Thompson’s group
复制标题
Thompson 群的 2 链和平方根
DOI：
10.1017/etds.2019.14
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发表时间：
2020
影响因子：
0.9
通讯作者：
LODHA, YASH
中科院分区：
文献类型：
--
作者：
KOBERDA, THOMAS;LODHA, YASH
研究了2-生成子群<$f，g <$< Homeo+（I），使得<$f2，g2 <$f同构于Thompson群F，且f和g的支撑构成两个区间的链.我们表明，这个类包含不可数许多同构类型。这些例子包括非阿贝尔自由子群，不承认忠实行动的C2同胚1流形的例子，不承认忠实行动的PL同胚的一个区间，和例子，没有提出。因此，我们回答了布林提出的问题。我们还表明，许多相对不复杂的同胚群可以有非常复杂的平方根，从而建立了F的平方根的行为作为一个普遍现象的一部分之间的子群的Homeo+（I）。
We study 2-generated subgroups〈 f, g〉< Homeo+(I) such that〈 f 2, g2〉 is isomorphic to Thompson’s group F, and such that the supports of f and g form a chain of two intervals. We show that this class contains uncountably many isomorphism types. These include examples with non-abelian free subgroups, examples which do not admit faithful actions by C2 diffeomorphisms on 1-manifolds, examples which do not admit faithful actions by PL homeomorphisms on an interval, and examples which are not finitely presented. We thus answer questions due to Brin. We also show that many relatively uncomplicated groups of homeomorphisms can have very complicated square roots, thus establishing the behavior of square roots of F as part of a general phenomenon among subgroups of Homeo+(I).