Minimal generating sets of Reidemeister moves - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: It is well known that any two diagrams representing the same oriented linkare related by a finite sequence of Reidemeister moves O1, O2 and O3. Dependingon orientations of fragments involved in the moves, one may distinguish 4different versions of each of the O1 and O2 moves, and 8 versions of the O3move. We introduce a minimal generating set of four oriented Reidemeistermoves, which includes two O1 moves, one O2 move, and one O3 move. We then studywhich other sets of up to 5 oriented moves generate all moves, and show thatonly few of them do. Some commonly considered sets are shown not to begenerating. An unexpected non-equivalence of different O3 moves is discussed.



Author: Michael Polyak

Source: https://arxiv.org/







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