Positive flow-spines and contact 3-manifolds

Ippei Ishii; Masaharu Ishikawa; Yuya Koda; Hironobu Naoe

Positive flow-spines and contact 3-manifolds

Ippei Ishii, Masaharu Ishikawa, Yuya Koda, Hironobu Naoe

Faculty of Economics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Journal	Unknown Journal
Publication status	Published - 2019 Dec 12

ASJC Scopus subject areas

General

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title = "Positive flow-spines and contact 3-manifolds",

abstract = "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)",

author = "Ippei Ishii and Masaharu Ishikawa and Yuya Koda and Hironobu Naoe",

year = "2019",

month = dec,

day = "12",

language = "English",

journal = "Mathematical Social Sciences",

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T1 - Positive flow-spines and contact 3-manifolds

AU - Ishii, Ippei

AU - Ishikawa, Masaharu

AU - Koda, Yuya

AU - Naoe, Hironobu

PY - 2019/12/12

Y1 - 2019/12/12

N2 - 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)

AB - 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)

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