Juan Pablo D'iaz

activity

20172025

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4 papers · 1 filter

math.GT2025

A Constructive Cubical Realization of $n$ -Dimensional Smooth Knots Inside the Menger $M_{n}^{n + 2}$ -continuum

Juan Pablo Díaz, Gabriela Hinojosa, Alberto Verjovsky

We prove that every smooth $n$ -dimensional knot in $R^{n + 2}$ can be ambiently isotoped into the Menger $n$ -dimensional continuum. In contrast with classical embedding theo…

math.GT2024

$N$ -dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group

Gabriela Hinojosa, Alberto Verjovsky, Juan Pablo Díaz

Starting with a smooth, non-trivial $n$ -dimensional knot $K\subset\bS^{n+2}$, and a beaded $n$ -dimensional necklace subordinated to $K$ , we construct a wild knot with a Cantor set…

math.GT2017

Cubulated moves for 2-knots

Juan Pablo Díaz, Gabriela Hinojosa, Alberto Verjovsky

In this paper, we prove that given two cubical links of dimension two in $R^{4}$ , they are isotopic if and only if one can pass from one to the other by a finite sequence o…

math.GT2017

Smoothing closed gridded surfaces embedded in $R^{4}$

Juan Pablo Díaz, Gabriela Hinojosa, Rogelio Valdez +1

We say that a topological $n$ -manifold $N$ is a cubical $n$ -manifold if it is contained in the $n$ -skeleton of the canonical cubulation $C$ of $R^{n + k}$ ($k\ge…

A Constructive Cubical Realization of n-Dimensional Smooth Knots Inside the Menger Mnn+2​-continuum

N-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group

Cubulated moves for 2-knots

Smoothing closed gridded surfaces embedded in R4

A Constructive Cubical Realization of $n$ -Dimensional Smooth Knots Inside the Menger $M_{n}^{n + 2}$ -continuum

$N$ -dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group

Smoothing closed gridded surfaces embedded in $R^{4}$