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

^*Corresponding author for this work

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

2 Citations (Scopus)

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.

Original language	English
Journal	Topology and its Applications
DOIs	https://doi.org/10.1016/j.topol.2015.05.041
Publication status	Accepted/In press - 2013 Sept 13

Keywords

Delta move
Handlebody-link
Linking number
Spatial graph

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2015.05.041

Cite this

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title = "A homotopy classification of two-component spatial graphs up to neighborhood equivalence",

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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author = "Atsuhiko Mizusawa and Ryo Nikkuni",

year = "2013",

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T1 - A homotopy classification of two-component spatial graphs up to neighborhood equivalence

AU - Mizusawa, Atsuhiko

AU - Nikkuni, Ryo

PY - 2013/9/13

Y1 - 2013/9/13

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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DO - 10.1016/j.topol.2015.05.041

M3 - Article

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SN - 0166-8641

JO - Topology and its Applications

JF - Topology and its Applications

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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