The group of boundary fixing homeomorphisms of the disc is not left-orderable
成果类型：
Article
署名作者：
Hyde, James
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2019.190.2.5
发表日期：
2019
页码：
657-661
关键词：
摘要：
A left-order on a group G is a total order < on G such that for any f, g and h in G we have f < g double left right arrow hf < hg. We construct a finitely generated subgroup H of Homeo(I-2; delta I-2), the group of those homeomorphisms of the disc that fix the boundary pointwise, and show H does not admit a left-order. Since any left-order on Homeo(I-2; delta I-2) would restrict to a left-order on H, this shows that Homeo(I-2; delta I-2) does not admit a left-order. Since Homeo(I; delta I) admits a left-order, it follows that neither H nor Homeo(I-2; delta I-2) embed in Homeo(I; delta I).