Smoothing closed gridded surfaces embedded in ℝ4-Reference-Cited by-同舟云学术

Smoothing closed gridded surfaces embedded in ℝ4

Published:2018-10 Issue:12 Volume:27 Page:1850065
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Díaz Juan Pablo¹,Hinojosa Gabriela²,Valdez Rogelio²,Verjovsky Alberto¹

Affiliation:

1. Instituto de Matemáticas, Unidad Cuernavaca., Universidad Nacional Autónoma de México., Av. Universidad s/n, Col. Lomas de Chamilpa., Cuernavaca, Morelos, México 62209, México

2. Centro de Investigación en Ciencias, IICBA. Universidad Autónoma del Estado de Morelos., Av. Universidad 1001, Col. Chamilpa. Cuernavaca, Morelos, México 62209, México

Abstract

We say that a topological [Formula: see text]-manifold [Formula: see text] is a cubical [Formula: see text]-manifold if it is contained in the [Formula: see text]-skeleton of the canonical cubulation [Formula: see text] of [Formula: see text] ([Formula: see text]). In this paper, we prove that any closed, oriented cubical [Formula: see text]-manifold has a transverse field of 2-planes in the sense of Whitehead and therefore it is smoothable by a small ambient isotopy.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216518500657

Reference11 articles.

1. Any smooth knot $\mathbb{S}^{n}\hookrightarrow\mathbb{R}^{n+2}$ is isotopic to a cubic knot contained in the canonical scaffolding of ℝ n+2

2. The topology of four-dimensional manifolds

3. Cubulations, immersions, mappability and a problem of habegger

4. CUBULATED MOVES AND DISCRETE KNOTS

5. A manifold which does not admit any differentiable structure

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