Lifting a generic surface in 3-space to an embedded surface in 4-space
type: Item
instance of: scholarly article
title: Lifting a generic surface in 3-space to an embedded surface in 4-space
zbMATH Open document ID: 0973.57009
DOI: 10.1016/S0166-8641(99)00074-7
author: Shin Satoh
published in: Topology and its Applications
publication date: 2001-11-29T00:00:00Z
review text: This paper treats the topic of knotted surfaces. It proves a necessary and sufficient condition when a generic surface in 3-space lifts to an embedded surface in 4-space. The given criterion is in terms of so-called black/white orientation (BW orientation). See the paper for the definition of BW orientation. The main result reads as follows: A generic surface in \(\mathbb{R}^3\) lifts to an embedded surface in \(\mathbb{R}^4\) if and only if its double point set admits a BW orientation. In the introduction of the article the author has listed the criteria that have preceded this one.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57Q35
zbMATH DE Number: 1501774
zbMATH Keywords: broken surface diagram
zbMATH Keywords: DP graph
zbMATH Keywords: BW orientation
zbMATH Keywords: double point set
zbMATH Keywords: knotted surfaces
reviewed by: Ivan Ivanšić
MaRDI profile type: Publication
full work available at URL: s0166-8641(99)00074-7
OpenAlex ID: W2017109017
description: scientific article; zbMATH DE number 1501774