Scholarlink

<p>We prove that any group acting faithfully on a bifoliated plane while preserving the orientations of both foliations is left-orderable. The proof utilizes a construction of a linear order on the set of ends of the leaf spaces, which takes advantage of the additional structure coming with a bifoliation. Moreover, we build an identification between ends of leaf spaces of the bifoliation and subsets of the boundary circle at infinity, and use it to give a condition for the equivalence between a faithful group action on a bifoliated plane and a faithful group action on the set of ends of the leaf spaces.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Left-orderability of groups acting on bifoliated planes

  • 期刊论文

  • 发表日期：

    2025年4月15日

查看全文
  • Mauro Camargo,
  • Lingfeng Lu

摘要

We prove that any group acting faithfully on a bifoliated plane while preserving the orientations of both foliations is left-orderable. The proof utilizes a construction of a linear order on the set of ends of the leaf spaces, which takes advantage of the additional structure coming with a bifoliation. Moreover, we build an identification between ends of leaf spaces of the bifoliation and subsets of the boundary circle at infinity, and use it to give a condition for the equivalence between a faithful group action on a bifoliated plane and a faithful group action on the set of ends of the leaf spaces.