Clasp-pass moves on knots, links and spatial graphs (Q1612276)

The authors consider clasp-pass moves, which are local moves on oriented links and spatial graphs. The graphs here are considered topologically, i.e. they are regarded as 1-simplicial complexes. The authors extend Habiro's result which states a necessary and sufficient condition for two knots to be transformed into each other by clasp-pass moves as having the same second coefficient of the Conway polynomial. They extend it to two-component links, three-component links, algebraically split links and spatial embeddings of a planar graph that does not contain disjoint cycles. They classify those in terms of linking numbers, the Arf invariant, the Milnor \(\mu\)-invariant and the second coefficient of the Conway polynomial.