Compatible Contact Structures of Fibered Positively Twisted Graph Multilinks in the 3-Sphere

Masaharu Ishikawa

doi:10.1007/s10013-014-0066-2

Compatible Contact Structures of Fibered Positively Twisted Graph Multilinks in the 3-Sphere

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

Abstract

We study compatible contact structures of fibered, positively twisted graph multilinks in S³ and prove that the contact structure of such a multilink is tight if and only if the orientations of its link components are all consistent with or all opposite to the orientation of the fibers of the Seifert fibrations of that graph multilink. As a corollary, we show that the compatible contact structures of the Milnor fibrations of real analytic germs of the form (Formula presented.) are always overtwisted.

Original language	English
Pages (from-to)	273-293
Number of pages	21
Journal	Vietnam Journal of Mathematics
Volume	42
Issue number	3
DOIs	https://doi.org/10.1007/s10013-014-0066-2
Publication status	Published - 2014 Sept 1
Externally published	Yes

Keywords

Contact structure
Milnor fibration
Open book decomposition

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10013-014-0066-2

Cite this

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title = "Compatible Contact Structures of Fibered Positively Twisted Graph Multilinks in the 3-Sphere",

abstract = "We study compatible contact structures of fibered, positively twisted graph multilinks in S3 and prove that the contact structure of such a multilink is tight if and only if the orientations of its link components are all consistent with or all opposite to the orientation of the fibers of the Seifert fibrations of that graph multilink. As a corollary, we show that the compatible contact structures of the Milnor fibrations of real analytic germs of the form (Formula presented.) are always overtwisted.",

keywords = "Contact structure, Milnor fibration, Open book decomposition",

author = "Masaharu Ishikawa",

note = "Publisher Copyright: {\textcopyright} 2014, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.",

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N2 - We study compatible contact structures of fibered, positively twisted graph multilinks in S3 and prove that the contact structure of such a multilink is tight if and only if the orientations of its link components are all consistent with or all opposite to the orientation of the fibers of the Seifert fibrations of that graph multilink. As a corollary, we show that the compatible contact structures of the Milnor fibrations of real analytic germs of the form (Formula presented.) are always overtwisted.

AB - We study compatible contact structures of fibered, positively twisted graph multilinks in S3 and prove that the contact structure of such a multilink is tight if and only if the orientations of its link components are all consistent with or all opposite to the orientation of the fibers of the Seifert fibrations of that graph multilink. As a corollary, we show that the compatible contact structures of the Milnor fibrations of real analytic germs of the form (Formula presented.) are always overtwisted.

KW - Contact structure

KW - Milnor fibration

KW - Open book decomposition

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JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 3

ER -

Compatible Contact Structures of Fibered Positively Twisted Graph Multilinks in the 3-Sphere

Abstract

Keywords

ASJC Scopus subject areas

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