A homotopy classification of two-component spatial graphs up to neighborhood equivalence

Atsuhiko Mizusawa; Ryo Nikkuni

doi:10.1016/j.topol.2015.05.041

A homotopy classification of two-component spatial graphs up to neighborhood equivalence

Atsuhiko Mizusawa^*, Ryo Nikkuni

^*この研究の対応する著者

研究成果: Article › 査読

1 被引用数 (Scopus)

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A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links.

本文言語	English
ジャーナル	Topology and its Applications
DOI	https://doi.org/10.1016/j.topol.2015.05.041
出版ステータス	Accepted/In press - 2013 9月 13

ASJC Scopus subject areas

幾何学とトポロジー

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10.1016/j.topol.2015.05.041

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abstract = "A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links.",

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AU - Mizusawa, Atsuhiko

AU - Nikkuni, Ryo

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N2 - A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links.

AB - A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links.

KW - Delta move

KW - Handlebody-link

KW - Linking number

KW - Spatial graph

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JO - Topology and its Applications

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ER -

A homotopy classification of two-component spatial graphs up to neighborhood equivalence

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