Collected mathematical papers. Volume 1 (1913--1932). Volume 2 (1932--1955). Ed. for the Danish Mathematical Society by Vagn Lundsgaard Hansen
type: Item
instance of: scholarly article
title: Collected mathematical papers. Volume 1 (1913--1932). Volume 2 (1932--1955). Ed. for the Danish Mathematical Society by Vagn Lundsgaard Hansen
zbMATH Open document ID: 0609.01050
published in: Contemporary Mathematicians
publication date: 1986-01-01T00:00:00Z
review text: Jakob Nielsen (1890--1959), one of the central figures of Danish mathematics in the first half of this century, is well known throughout the international mathematical community for his pioneering work and remarkable achievements in combinatorial group theory and the topology of surfaces. The recent revival of the theory of surface transformations has led to a renewed strong interest in his original methods and results. The decision taken by the Danish Mathematical Society to make his original papers available to a wider audience must therefore be greeted with satisfaction. These two volumes contain a selection of 33 from Nielsen's 46 published papers (two of them coauthored by S. Bundgaard and one by W. Fenchel) and also a set of notes from his inaugural lectures in Breslau in 1921. From these, 11 papers, including Nielsen's dissertation (presented to the University of Kiel in 1912 and published in 1913), appear in their original German version; 7 papers, originally published in German and including the Breslau notes and his four long memoirs in ''Acta Mathematica'' from 1927 [Acta Math. 50, 189--358 (1927; JFM 53.0545.12)], 1929 [ibid. 53, 1--76 (1929; JFM 55.0971.01)], 1932 [ibid. 58, 87--167 (1932; Zbl 0004.27501)] and 1942 [ibid. 75, 23--115 (1942; Zbl 0027.26601)] which present his pioneering work on surface transformations, appear here in John Stillwell's English translation; other 10 papers, originally published in Danish and including the famous paper on free groups from 1921, also appear in English translation (one by Anne W. Neumann, one by Hans J. Munkholm, and the others by J. Stillwell); the remaining 6 papers (one in French and 5 in English) are reproduced in their original version. Volume 1 opens with Werner Fenchel's memorial paper which presents Nielsen's life and mathematical achievements; it includes a complete list of Nielsen's publications. Volume 2 concludes with the following 5 essays: \textit{Bruce Chandler} and \textit{Wilhelm Magnus} - ''T…
reviewed by: J.Weinstein
Mathematics Subject Classification ID: 01A75
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 3985183
zbMATH Keywords: combinatorial group theory
zbMATH Keywords: topology of surfaces
zbMATH Keywords: surface transformations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3985183