TY - JOUR
T1 - Clasp-pass moves on knots, links and spatial graphs
AU - Taniyama, Kouki
AU - Yasuhara, Akira
PY - 2002/8/16
Y1 - 2002/8/16
N2 - A clasp-pass move is a local move on oriented links introduced by Habiro in 1993. He showed that two knots are transformed into each other by clasp-pass moves if and only if they have the same second coefficient of the Conway polynomial. We extend his classification to two-component links, three-component links, algebraically split links, and spatial embeddings of a planar graph that does not contain disjoint cycles. These are classified in terms of linking numbers, the second coefficient of the Conway polynomial, the Arf invariant, and the Milnor μ-invariant.
AB - A clasp-pass move is a local move on oriented links introduced by Habiro in 1993. He showed that two knots are transformed into each other by clasp-pass moves if and only if they have the same second coefficient of the Conway polynomial. We extend his classification to two-component links, three-component links, algebraically split links, and spatial embeddings of a planar graph that does not contain disjoint cycles. These are classified in terms of linking numbers, the second coefficient of the Conway polynomial, the Arf invariant, and the Milnor μ-invariant.
KW - Clasp-pass move
KW - Delta move
KW - Spatial graph
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U2 - 10.1016/S0166-8641(01)00189-4
DO - 10.1016/S0166-8641(01)00189-4
M3 - Article
AN - SCOPUS:0038013679
VL - 122
SP - 501
EP - 529
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 3
ER -