Homology classification of spatial graphs by linking numbers and Simon invariants

Reiko Shinjo; Kouki Taniyama

doi:10.1016/S0166-8641(03)00101-9

Homology classification of spatial graphs by linking numbers and Simon invariants

Reiko Shinjo, Kouki Taniyama^*

^*Corresponding author for this work

School of Education

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

7 Citations (Scopus)

Abstract

We show that two embeddings f and g of a finite graph G into the 3-space are spatial-graph-homologous if and only if for each subgraph H of G that is homeomorphic to a disjoint union of two circles, the restriction maps f _H and g _H have the same linking number, and for each subgraph H of G that is homeomorphic to a complete graph K₅ or a complete bipartite graph K_3,3, the restriction maps f _H and g _H have the same Simon invariant.

Original language	English
Pages (from-to)	53-67
Number of pages	15
Journal	Topology and its Applications
Volume	134
Issue number	1
DOIs	https://doi.org/10.1016/S0166-8641(03)00101-9
Publication status	Published - 2003 Oct 15

Keywords

Delta move
Finite type invariant
Linking number
Simon invariant
Spatial graph
Spatial-graph-homology

ASJC Scopus subject areas

Geometry and Topology

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10.1016/S0166-8641(03)00101-9

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AB - We show that two embeddings f and g of a finite graph G into the 3-space are spatial-graph-homologous if and only if for each subgraph H of G that is homeomorphic to a disjoint union of two circles, the restriction maps f H and g H have the same linking number, and for each subgraph H of G that is homeomorphic to a complete graph K5 or a complete bipartite graph K3,3, the restriction maps f H and g H have the same Simon invariant.

KW - Delta move

KW - Finite type invariant

KW - Linking number

KW - Simon invariant

KW - Spatial graph

KW - Spatial-graph-homology

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Homology classification of spatial graphs by linking numbers and Simon invariants

Abstract

Keywords

ASJC Scopus subject areas

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