Every smooth n-knot in R^{n+2} can be ambiently isotoped into the Menger n-continuum via cubical models combining prior realization theorems with affine self-similarity.
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Explicit recursive constructions produce infinitely many non-equivalent wild knots in the Menger sponge whose wild points lie in a Cantor set, and dynamically defined wild knots from Kleinian actions can be isotoped into the sponge.
citing papers explorer
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A Constructive Cubical Realization of $n$-Dimensional Smooth Knots Inside the Menger $M^{n+2}_n$-continuum
Every smooth n-knot in R^{n+2} can be ambiently isotoped into the Menger n-continuum via cubical models combining prior realization theorems with affine self-similarity.
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Wild knots embedded in the Menger Sponge
Explicit recursive constructions produce infinitely many non-equivalent wild knots in the Menger sponge whose wild points lie in a Cantor set, and dynamically defined wild knots from Kleinian actions can be isotoped into the sponge.