On the Necessity of Reidemeister Moves
نویسنده
چکیده
We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister Ω2-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.
منابع مشابه
On the Necessity of Reidemeister Move 2 for Simplifying Immersed Planar Curves
In 2001, 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.
متن کاملMinimal Sets of Reidemeister Moves
It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves Ω1, Ω2 and Ω3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the Ω1 and Ω2 moves, and 8 versions of the Ω3 move. We introduce a minimal generating set of four oriented Reidemeister moves, which inclu...
متن کاملA Lower Bound for the Number of Reidemeister Moves for Unknotting
How many Reidemeister moves do we need for unknotting a given diagram of the trivial knot? Hass and Lagarias gave an upper bound. We give an upper bound for deforming a diagram of a split link to be disconnected. On the other hand, the absolute value of the writhe gives a lower bound of the number of Reidemeister I moves for unknotting. That of a complexity of knot diagram “cowrithe” works for ...
متن کاملA Jones polynomial for braid-like isotopies of oriented links and its categorification
Links in 3–space are usually given by diagrams and isotopies of links by sequences of Reidemeister moves (see e.g. [BZ85]). For relatively oriented links (i.e. up to global orientation reversing), there are exactly two different local (i.e. without regarding the rest of the diagram) Reidemeister moves of type II , shown in Figure 1, and eight local Reidemeister moves of type III , shown in Figu...
متن کاملA Lower Bound for the Number of Reidemeister Moves of Type Iii
We study the number of Reidemeister type III moves using Fox n-colorings of knot diagrams.
متن کامل