Positive flow-spines and contact 3-manifolds

Ippei Ishii, Masaharu Ishikawa, Yuya Koda, Hironobu Naoe

Research output: Contribution to journalArticlepeer-review


We say that a contact structure on a closed, connected, oriented, smooth 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. We then define a map from the set of positive flow-spines to the set of contact 3-manifolds up to contactomorphism by sending a positive flow-spine to the supported contact 3-manifold and show that this map is well-defined and surjective. We also determine the contact 3-manifolds supported by positive flow-spines with up to 3 vertices. As an application, we introduce the complexity for contact 3-manifolds and determine the contact 3-manifolds with complexity up to 3.

MSC Codes 57M50 (Primary) 37C27, 57M25, 57Q15 (Secondary)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Dec 12

ASJC Scopus subject areas

  • General

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