Chorlay, Renaud (Author)
Revue d'Histoire des Mathématiques
Volume: 15
Pages: 231--316
Edition Details: Translated title: [Going Global: The Case of Élie Cartan, 1922--1930.] In French.
Language: French
After his work on connections and generalized spaces between 1922 and 1925, Élie Cartan began laying the foundation of the topological and geometric study of Lie groups and homogeneous spaces (1925--1930). We will endeavour to establish that the emergence of global questions is but part and parcel of a thorough restructuring around the epistemological polarity between local and global, a restructuring that occurs at three levels : a theoretical level, a thematic level and a rhetorical level. This new central polarity replaced a 19th century polarity between the infinitesimal and the finite. Our chronological exposition of Cartan's work in the period between 1922 and 1930 will pay special attention to modes of writing, comparing with the works of Hermann Weyl and Otto Schreier. We shall see, in particular, that in spite of the stability of terms such as ``neighbourhood'', ``manifold'' or ``group'', the meaning of these words underwent a dramatic change after 1925.
...MoreDescription On Cartan's work on the topological and geometric study of Lie groups and homogeneous spaces.
Similar Citations
Article
A. Cogliati;
P. Mastrolia;
(2018)
Cartan, Schouten and the Search for Connection
(/isis/citation/CBB215046326/)
Article
Nabonnand, Philippe;
(2009)
La notion d'holonomie chez Élie Cartan
(/isis/citation/CBB000954526/)
Book
Hawkins, Thomas;
(2000)
Emergence of the theory of Lie groups: An essay in the history of mathematics, 1869-1926
(/isis/citation/CBB000110932/)
Article
Cogliati, Alberto;
(2011)
On the Genesis of the Cartan--Kähler Theory
(/isis/citation/CBB001034289/)
Book
Chorlay, Renaud;
(2015)
Géométrie et topologie différentielles, 1918-1932
(/isis/citation/CBB224758445/)
Article
Moore, Gregory H.;
(2007)
The Evolution of the Concept of Homeomorphism
(/isis/citation/CBB000772446/)
Article
Yan, Chenguang;
Deng, Mingli;
(2011)
The Contribution of Chevalley to the Class Field Theory
(/isis/citation/CBB001210024/)
Article
Rodríguez, Laura;
(2015)
Frigyes Riesz and the Emergence of General Topology
(/isis/citation/CBB001202211/)
Article
German A. Duarte;
(2017)
"Analysis Situs." A Survey of Spaces en devenir
(/isis/citation/CBB765530267/)
Book
Epple, Moritz;
(1999)
Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie
(/isis/citation/CBB000650718/)
Article
Ji, Lizhen;
Papadopoulos, Athanase;
(2013)
Historical Development of Teichmüller theory
(/isis/citation/CBB001252702/)
Article
Ullrich, Peter;
(2000)
The Poincaré-Volterra Theorem: From Hyperelliptic Integrals to Manifolds with Countable Topology
(/isis/citation/CBB000740287/)
Article
McLarty, Colin;
(2005)
Poor Taste as a Bright Character Trait: Emmy Noether and the Independent Social Democratic Party
(/isis/citation/CBB000651667/)
Article
Chris Meyns;
(2020)
‘Data’ in the Royal Society's Philosophical Transactions, 1665–1886
(/isis/citation/CBB598614888/)
Book
Audin, Michèle;
(2012)
Jacques Feldbau, Topologe: Das Schicksal eines Jüdischen Mathematikers (1914--1945)
(/isis/citation/CBB001214133/)
Article
Lewis, Albert C.;
(2004)
The Beginnings of the R. L. Moore School of Topology
(/isis/citation/CBB000470917/)
Article
Berrone, Lucio R.;
(2006)
Un manuscrito inédito de Beppo Levi
(/isis/citation/CBB000930262/)
Chapter
Marquis, Jean-Pierre;
(2006)
A Path to the Epistemology of Mathematics: Homotopy Theory
(/isis/citation/CBB000800124/)
Book
Dalen, Dirk van;
(2013)
L. E. J. Brouwer: Topologist, Intuitionist, Philosopher---How Mathematics is Rooted in Life
(/isis/citation/CBB001500395/)
Article
Moore, Gregory H.;
(2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology
(/isis/citation/CBB000950203/)
Be the first to comment!