On the necessity of Reidemeister move 2 for simplifying immersed planar curves
Tobias Hagge ; Jonathan Yazinski
Banach Center Publications, Tome 102 (2014), p. 101-110 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:282358 
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     title = {On the necessity of Reidemeister move 2 for simplifying immersed planar curves},
     journal = {Banach Center Publications},
     volume = {102},
     year = {2014},
     pages = {101-110},
     zbl = {1314.14055},
     language = {en},
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Tobias Hagge; Jonathan Yazinski. On the necessity of Reidemeister move 2 for simplifying immersed planar curves. Banach Center Publications, Tome 102 (2014) pp. 101-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-4/