Property P for the band-connect sum of two knots
type: Item
instance of: scholarly article
title: Property P for the band-connect sum of two knots
zbMATH Open document ID: 0628.57005
DOI: 10.1016/0040-9383(87)90060-7
published in: Topology
publication date: 1987-01-01T00:00:00Z
review text: The author proves that the nontrivial band-sum of two knots has property P. This theorem implies immediately the affirmative solution to a long- standing conjecture (solved first by Scharlemann) that if a band-sum of two knots \(K_ 1\) and \(K_ 2\) is the unknot, then \(K_ 1\) and \(K_ 2\) are both the unknot and a band is also trivial. The proof of the theorem is short, but needs deep results due to D. Gabai.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4022164
zbMATH Keywords: band-sum of two knots
zbMATH Keywords: property P
author: Abigail Thompson
reviewed by: K. Murasugi
MaRDI profile type: Publication
full work available at URL: 0040-9383(87)90060-7
OpenAlex ID: W1964825957
description: scientific article; zbMATH DE number 4022164