L'oeuvre mathématique de Louis Antoine et son influence. (The mathematical work of Louis Antoine and its influence)
type: Item
instance of: scholarly article
title: L'oeuvre mathématique de Louis Antoine et son influence. (The mathematical work of Louis Antoine and its influence)
zbMATH Open document ID: 0734.01013
author: N. E. Zubov
published in: Expositiones Mathematicae
publication date: 1991-01-01T00:00:00Z
review text: 1988 marked the 100th anniversary of the birth of the French topologist Louis Antoine. This account begins with a synopsis of his life which draws on G. Julia's 1971 obituary notice to tell how Henri Lebesgue pointed the blind Antoine in the direction of the topology of 2 and 3 dimensions because there was only a small bibliography that had to be copied into Braille and partly because ``in such a study the eyes of the spirit and the habit of concentration will replace the lost vision.'' Antoine's 1921 thesis presented a particular method for constructing a certain subset of \(R^ 3\) which became known as Antoine's ``necklace''. An amply illustrated and detailed explanation of Antoine's construction is given. This was a strong influence on J. W. Alexander's work on the Horned sphere in 1923 and his disproof of Schoenflies conjecture for dimension 3. This in turn led to Morton Brown's complete solution of the problem for locally flat embeddings in 1960. Antoine's necklace inspired a key demonstration in R. H. Bing's work in 1952 which led to the fruitful Bing shrinking criterion. A 23-item bibliography covering works from 1908 to 1982 rounds off the account.
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 54-03
zbMATH DE Number: 4213938
zbMATH Keywords: Antoine's necklace
zbMATH Keywords: Schoenflies problem
zbMATH Keywords: Bing shrinking criterion
zbMATH Keywords: Henri Lebesgue
zbMATH Keywords: J. W. Alexander
zbMATH Keywords: Morton Brown
reviewed by: Albert C. Lewis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4213938