TY - JOUR
T1 - Homology classification of spatial graphs by linking numbers and Simon invariants
AU - Shinjo, Reiko
AU - Taniyama, Kouki
PY - 2003/10/15
Y1 - 2003/10/15
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=0042381265&partnerID=8YFLogxK
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U2 - 10.1016/S0166-8641(03)00101-9
DO - 10.1016/S0166-8641(03)00101-9
M3 - Article
AN - SCOPUS:0042381265
SN - 0166-8641
VL - 134
SP - 53
EP - 67
JO - Topology and its Applications
JF - Topology and its Applications
IS - 1
ER -