Displaying similar documents to “Delta link-homotopy on spatial graphs.”

Link homotopy invariants of graphs in R.

Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we define a link homotopy invariant of spatial graphs based on the second degree coefficient of the Conway polynomial of a knot.

Sharp edge-homotopy on spatial graphs.

Ryo Nikkuni (2005)

Revista Matemática Complutense

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A sharp-move is known as an unknotting operation for knots. A self sharp-move is a sharp-move on a spatial graph where all strings in the move belong to the same spatial edge. We say that two spatial embeddings of a graph are sharp edge-homotopic if they are transformed into each other by self sharp-moves and ambient isotopies. We investigate how is the sharp edge-homotopy strong and classify all spatial theta curves completely up to sharp edge-homotopy. Moreover we mention a relationship...

Pure virtual braids homotopic to the identity braid

H. A. Dye (2009)

Fundamenta Mathematicae

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Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing changes. We recall the pure virtual braid group. We then describe the set of pure virtual braids that are homotopic to the identity braid.

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

Tobias Hagge, Jonathan Yazinski (2014)

Banach Center Publications

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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.