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LSpice
LSpice
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I think your description of a knot as a string with endpoints pulled apart is similar to embedding knots in $\mathbb{RP}^3$, with the free endpoints corresponding to a single point on $\mathbb{R}^3$'s boundary. There are several papers on knots in $\mathbb{RP}^3$. The most notable related knots in $\mathbb{RP}^3$ to knots in $\mathbb{R}^3$ by sliding a small reflecting sphere along the knot and looking at the knot's reflection. IIRC, there are examples of unknots in \mathbb{R}^3$$\mathbb{R}^3$ that cannot be untied monotonically.

I think your description of a knot as a string with endpoints pulled apart is similar to embedding knots in $\mathbb{RP}^3$, with the free endpoints corresponding to a single point on $\mathbb{R}^3$'s boundary. There are several papers on knots in $\mathbb{RP}^3$. The most notable related knots in $\mathbb{RP}^3$ to knots in $\mathbb{R}^3$ by sliding a small reflecting sphere along the knot and looking at the knot's reflection. IIRC, there are examples of unknots in \mathbb{R}^3$ that cannot be untied monotonically.

I think your description of a knot as a string with endpoints pulled apart is similar to embedding knots in $\mathbb{RP}^3$, with the free endpoints corresponding to a single point on $\mathbb{R}^3$'s boundary. There are several papers on knots in $\mathbb{RP}^3$. The most notable related knots in $\mathbb{RP}^3$ to knots in $\mathbb{R}^3$ by sliding a small reflecting sphere along the knot and looking at the knot's reflection. IIRC, there are examples of unknots in $\mathbb{R}^3$ that cannot be untied monotonically.

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Michael
Michael
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I think your description of a knot as a string with endpoints pulled apart is similar to embedding knots in $\mathbb{RP}^3$, with the free endpoints corresponding to a single point on $\mathbb{R}^3$'s boundary. There are several papers on knots in $\mathbb{RP}^3$. The most notable related knots in $\mathbb{RP}^3$ to knots in $\mathbb{R}^3$ by sliding a small reflecting sphere along the knot and looking at the knot's reflection. IIRC, there are examples of unknots in \mathbb{R}^3$ that cannot be untied monotonically.