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Ck-moves on spatial theta-curves and Vassiliev invariants
by
Akira Yasuhara
Tokyo Gakugei University and George Washington University
The Ck-equivalence is an equivalence relation generated by Ck-moves defined by Habiro. Habiro showed that the set of Ck-equivalence classes of the knots forms an abelian group under the connected sum and it can be classified by the additive Vassiliev invariant of order≤ k-1. We see that the set of Ck-equivalence classes of the spatial \theta-curves forms a group under the vertex connected sum and that if the group is abelian, then it can be classified by the additive Vassiliev invariant of order≤ k-1. However the group is not necessarily abelian. In fact, we show that it is nonabelian for k ≥ 12. As an easy consequence, we have the set of Ck-equivalence classes of m-string links, which forms a group under the composition, is nonabelian for k ≥ 12 and m ≥ 2.
Date received: April 27, 2001
Copyright © 2001 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cahj-04.