Positive flow-spines and contact 3-manifolds, II

Ippei Ishii; Masaharu Ishikawa; Yuya Koda; Hironobu Naoe

doi:10.1007/s10231-023-01400-4

Positive flow-spines and contact 3-manifolds, II

Ippei Ishii, Masaharu Ishikawa, Yuya Koda, Hironobu Naoe

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

Abstract

In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively.

Original language	English
Pages (from-to)	1251-1266
Number of pages	16
Journal	Annali di Matematica Pura ed Applicata
Volume	203
Issue number	3
DOIs	https://doi.org/10.1007/s10231-023-01400-4
Publication status	Published - 2024 Jun

Keywords

3-Dimensional manifold
57Q15
Contact structure
Flow
Polyhedron
Primary 57K33
Secondary 57M50
Spine

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10231-023-01400-4

Cite this

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abstract = "In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively.",

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AU - Ishikawa, Masaharu

AU - Koda, Yuya

AU - Naoe, Hironobu

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KW - Contact structure

KW - Flow

KW - Polyhedron

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Positive flow-spines and contact 3-manifolds, II

Abstract

Keywords

ASJC Scopus subject areas

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