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.

引用

页码：885 / 897

页数：13

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