On the necessity of Reidemeister move 2 for simplifying immersed planar curves
Volume 103 / 2014
Banach Center Publications 103 (2014), 101-110
MSC: Primary 14H50.
DOI: 10.4064/bc103-0-4
Abstract
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 $S^{1} \rightarrow\mathbb{R}^{2}$ to the standard embedding of the circle. We show that this conjecture is false.
