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On the necessity of Reidemeister move 2 for simplifying immersed planar curves

Tobias Hagge; Jonathan Yazinski — 2014

Banach Center Publications

In 2001, motivated by his results on finite-type knot diagram invariants, Östlund conjectured that Reidemeister moves 1 and 3 are sufficient to describe a homotopy from any generic immersion S¹ → ℝ² to the standard embedding of the circle. We show that this conjecture is false.

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