A projective plane in \({\mathbb{R}}^ 4\) with three critical points is standard. Strongly invertible knots have property P
type: Item
instance of: scholarly article
title: A projective plane in \({\mathbb{R}}^ 4\) with three critical points is standard. Strongly invertible knots have property P
zbMATH Open document ID: 0678.57003
DOI: 10.1016/0040-9383(88)90030-4
author: Steven A. Bleiler
author: Martin Scharlemann
published in: Topology
publication date: 1988-01-01T00:00:00Z
review text: The main result of this paper is that if one gets the unknot by attaching a band to the unknot, then the band is a trivial band with a half twist. The proof uses variations on the combinatorics of the intersection of planar surfaces developed by the second author [Invent. Math. 79, 125-141 (1985; Zbl 0559.57019) and ibid. 82, 37-55 (1985; Zbl 0576.57004)] and which have turned out to be very important elsewhere in 3-manifold topology - e.g. in the solution of the knot complement problem and in the cyclic surgery theorem. The theorems of the title are derived as consequences.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 4111598
zbMATH Keywords: projective plane in \({\mathbb{R}}^ 4\)
zbMATH Keywords: critical point
zbMATH Keywords: strongly invertible knots
zbMATH Keywords: property P
zbMATH Keywords: attaching a band to the unknot
zbMATH Keywords: trivial band with a half twist
MaRDI profile type: Publication
full work available at URL: 0040-9383(88)90030-4
OpenAlex ID: W1988800780
description: scientific article; zbMATH DE number 4111598