ON THE PERFECTNESS OF GROUPS OF DIFFEOMORPHISMS OF THE INTERVAL TANGENT TO THE IDENTITY AT THE ENDPOINTS
ON THE PERFECTNESS OF GROUPS OF DIFFEOMORPHISMS OF THE INTERVAL TANGENT TO THE IDENTITY AT THE ENDPOINTS
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论端点处恒等式切线区间微分形群的完备性
DOI：
10.1142/9789812778246_0022
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
T. Tsuboi
中科院分区：
文献类型：
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作者：
T. Tsuboi
本文证明了闭区间上的几个保向同胚群是完美的，即群中的每个元素都可表示为一个算子的乘积。结果可能不是新的，但证明方法会令人感兴趣。方法是将一个元素写成元素的积，这些元素是累积到端点的子区间上的单位元。然后有许多情况下，后者是产品的制冷剂。这样，我们证明了同胚群、Lipschitz同胚群、在端点处与恒等式相切的C ∞同胚群以及在端点处与恒等式无限相切的C∞同胚群的完备性。
This paper shows that several groups of orientation preserving homeomorphisms of the closed interval are perfect, that is, every element of the group is written as a product of commutators. Results might not be new, however the method of proof would be of interest. The method is to write an element as a product of elements which are the identity on subintervals accumulating to the end points. Then there are many cases where the latters are products of commutators. In this way, we show the perfectness of the group of homeomorphisms, of the group of Lipschitz homeomorphisms, of the group of the C1diffeomorphisms which are tangent to the identity at the endpoints, and of the group of the C∞diffeomorphisms which are infinitely tangent to the identity at the endpoints.