On the connectedness of the space of codimension one foliations on a closed 3-manifold

• 成果类型: Article
• 署名作者: Eynard-Bontemps, Helene
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0622-8
• 发表日期: 2016
• 页码: 605-670
• 关键词: leaves

摘要

We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late 60's that every plane field can be deformed continuously to an integrable one, so the above inclusion induces a surjective map between connected components. We prove that this map is actually a bijection.