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On non-self local moves. (English) Zbl 1244.57021
The authors study a special class of $$C_m$$ moves, called non-self $$C_m$$ moves, and show that for any positive integer $$m$$, two links can be transformed into each other by a finite sequence of non-self $$C_m$$ moves if and only if (1) the two links can be transformed into each other by a finite sequence of $$C_m$$ moves and (2) the knot types of corresponding components coincide.
##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)
##### Keywords:
local move; linking number; knot type
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##### References:
 [1] M. Gusarov, Topology of Manifolds and Varieties, ed. O. Viro (American Mathematical Society, Providence, 1994) pp. 173–192. [2] DOI: 10.2140/gt.2000.4.1 · Zbl 0941.57015 · doi:10.2140/gt.2000.4.1 [3] Taniyama K., Math. Proc. Cambridge Philos. Soc. 133 pp 325–
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