Reversibility in the group of homeomorphisms of the circle

被引：7
|
作者：
Gill, Nick [1 ]
O'Farrell, Anthony G. [2 ]
Short, Ian [3 ]
机构：
[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
[2] Natl Univ Ireland Maynooth, Dept Math, Maynooth, Kildare, Ireland
[3] Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2009年 / 41卷
基金：
爱尔兰科学基金会;
关键词：
D O I：
10.1112/blms/bdp065
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The group of orientation-preserving homeomorphisms of the circle is simple, and, because there are non-trivial involutions in this group, it must be generated by its involutions. We show that, in this group of homeomorphisms, each element can be expressed as a product of three involutions. We also characterise those elements of the group that can be expressed as a composite of two involutions, and perform a similar characterisation in the full group of homeomorphisms of the circle.
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页码：885 / 897
页数：13
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