Positive flow-spines and contact 3-manifolds

Ippei Ishii, Masaharu Ishikawa, Yuya Koda, Hironobu Naoe

研究成果: Article査読


A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper.

ジャーナルAnnali di Matematica Pura ed Applicata
出版ステータスAccepted/In press - 2023

ASJC Scopus subject areas

  • 応用数学


「Positive flow-spines and contact 3-manifolds」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。