Every Reidemeister move is needed for each knot type

Details Every Reidemeister move is needed for each knot type Every Reidemeister move is needed for each knot type

2004-04-07

arxiv.org/abs/math/0404145v2

Mathematics

Geometric Topology

8 pages, 8 figures. Changed title and added mention of a partial result by Vassily Manturov

Scientific paper

We show that every knot type admits a pair of diagrams that cannot be made
identical without using Reidemeister Omega_2-moves. We also show that our proof
is compatible with known results for the other move types, in the sense that
every knot type admits a pair of diagrams that cannot be made identical without
using all of the move types.

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