On the finiteness of higher knot sums
type: Item
instance of: scholarly article
title: On the finiteness of higher knot sums
zbMATH Open document ID: 0623.57013
DOI: 10.1016/0040-9383(87)90005-X
author: M. J. Dunwoody
author: Roger Fenn
published in: Topology
publication date: 1987-01-01T00:00:00Z
review text: This paper settles a long-standing problem in high-dimensional knot theory by showing that every \(n\)-knot (n\(\geq 3)\) decomposes as a sum of irreducible knots, and that for a given knot there is a finite upper bound on the number of summands. The proof is a beautiful application of the theory of groups acting on trees.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57S99
zbMATH DE Number: 4011443
zbMATH Keywords: decompositions of the knot group
zbMATH Keywords: n-knot
zbMATH Keywords: sum of irreducible knots
zbMATH Keywords: upper bound on the number of summands
zbMATH Keywords: groups acting on trees
reviewed by: C. Kearton
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4011443