Homology classification of spatial graphs by linking numbers and Simon invariants

Reiko Shinjo, Kouki Taniyama

Research output: Contribution to journalArticle

8 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 K3,3, the restriction maps f H and g H have the same Simon invariant.

Original languageEnglish
Pages (from-to)53-67
Number of pages15
JournalTopology and its Applications
Volume134
Issue number1
DOIs
Publication statusPublished - 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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