a history of early algebraic topology · a history of early algebraic topology john mccleary,...
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![Page 1: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/1.jpg)
A History of Early Algebraic Topology
John McCleary, Vassar College
June 6, 2013
![Page 2: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/2.jpg)
Toutes les voiesdiverses ou je m’etaisengage successivementme conduisaienta l’Analysis Situs.
Henri Poincare 1895
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La situation d’abord du vingtieme siecle
1) La croissance d’importance de l’abstraction
2) La fondation des centres d’activite; les grandes ecoles
3) L’anxiete sur les erreurs
![Page 4: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/4.jpg)
La situation d’abord du vingtieme siecle
1) La croissance d’importance de l’abstraction
2) La fondation des centres d’activite; les grandes ecoles
3) L’anxiete sur les erreurs
![Page 5: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/5.jpg)
La situation d’abord du vingtieme siecle
1) La croissance d’importance de l’abstraction
2) La fondation des centres d’activite; les grandes ecoles
3) L’anxiete sur les erreurs
![Page 6: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/6.jpg)
La situation d’abord du vingtieme siecle
1) La croissance d’importance de l’abstraction
2) La fondation des centres d’activite; les grandes ecoles
3) L’anxiete sur les erreurs
![Page 7: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/7.jpg)
Hermann Weyl (1885–1955)
Analisis situs combinatorio, Revista MathematicaHispano-Americana, 5(1923), 43–69; 6(1924), 1–9, 33–41.
“The subject matter was not serious mathematics.”
![Page 8: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/8.jpg)
Hermann Weyl (1885–1955)
Analisis situs combinatorio, Revista MathematicaHispano-Americana, 5(1923), 43–69; 6(1924), 1–9, 33–41.
“The subject matter was not serious mathematics.”
![Page 9: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/9.jpg)
B. L. van der Waerden (1903–1996)
Combinatorial topology was a “battlefield of differing methods . . . .”
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B. L. van der Waerden (1903–1996)
Combinatorial topology was a “battlefield of differing methods . . . .”
![Page 11: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/11.jpg)
L. E. J. Brouwer (1881–1966)
. . . given the incompatibility of our views on fundamental matters,
. . . we will forgo your co-operation in the editing of the Annalen andthus delete your name from the title page.
Hilbert
. . . and editor of the Annalen, I have always considered myself obligedto reserve a large part of my time on behalf of coming youngmathematicians, . . .
Brouwer
![Page 12: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/12.jpg)
L. E. J. Brouwer (1881–1966)
. . . given the incompatibility of our views on fundamental matters,
. . . we will forgo your co-operation in the editing of the Annalen andthus delete your name from the title page.
Hilbert
. . . and editor of the Annalen, I have always considered myself obligedto reserve a large part of my time on behalf of coming youngmathematicians, . . .
Brouwer
![Page 13: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/13.jpg)
Sur les courbes definies par une equation differentielle (troisiemepartie), Journal des Math. (4)1)(1885), 167–244.
A
B
P M
N
ind. cycle =e − i − 2
2ind. APBMA = ind. ANBMA + ind. APBNA.
#noeuds −#cols −#foyers = χ(S).
![Page 14: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/14.jpg)
Sur les courbes definies par une equation differentielle (troisiemepartie), Journal des Math. (4)1)(1885), 167–244.
A
B
P M
N
ind. cycle =e − i − 2
2ind. APBMA = ind. ANBMA + ind. APBNA.
#noeuds −#cols −#foyers = χ(S).
![Page 15: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/15.jpg)
![Page 16: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/16.jpg)
Selon Poincare, une variete est:
1) comme l’ensemble des pointes reguliers qui satisfient une systemedes egalites et inegalites des fonctions differentielles de n variables
2) comme une chaine des domaines parametrizes par fonctionsanalytique (de maniere de la continuation analytique)
3) comme une somme des polyedres qui satisfait particuliersconditions
4) comme les methodes de Heegaard (diagrams de Heegaard)
Il a introduit les outils de la cobordisme, l’homologie, le groupefundamental, l’idee de homeomorphisme . . . .
![Page 17: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/17.jpg)
Selon Poincare, une variete est:
1) comme l’ensemble des pointes reguliers qui satisfient une systemedes egalites et inegalites des fonctions differentielles de n variables
2) comme une chaine des domaines parametrizes par fonctionsanalytique (de maniere de la continuation analytique)
3) comme une somme des polyedres qui satisfait particuliersconditions
4) comme les methodes de Heegaard (diagrams de Heegaard)
Il a introduit les outils de la cobordisme, l’homologie, le groupefundamental, l’idee de homeomorphisme . . . .
![Page 18: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/18.jpg)
Selon Poincare, une variete est:
1) comme l’ensemble des pointes reguliers qui satisfient une systemedes egalites et inegalites des fonctions differentielles de n variables
2) comme une chaine des domaines parametrizes par fonctionsanalytique (de maniere de la continuation analytique)
3) comme une somme des polyedres qui satisfait particuliersconditions
4) comme les methodes de Heegaard (diagrams de Heegaard)
Il a introduit les outils de la cobordisme, l’homologie, le groupefundamental, l’idee de homeomorphisme . . . .
![Page 19: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/19.jpg)
Selon Poincare, une variete est:
1) comme l’ensemble des pointes reguliers qui satisfient une systemedes egalites et inegalites des fonctions differentielles de n variables
2) comme une chaine des domaines parametrizes par fonctionsanalytique (de maniere de la continuation analytique)
3) comme une somme des polyedres qui satisfait particuliersconditions
4) comme les methodes de Heegaard (diagrams de Heegaard)
Il a introduit les outils de la cobordisme, l’homologie, le groupefundamental, l’idee de homeomorphisme . . . .
![Page 20: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/20.jpg)
Selon Poincare, une variete est:
1) comme l’ensemble des pointes reguliers qui satisfient une systemedes egalites et inegalites des fonctions differentielles de n variables
2) comme une chaine des domaines parametrizes par fonctionsanalytique (de maniere de la continuation analytique)
3) comme une somme des polyedres qui satisfait particuliersconditions
4) comme les methodes de Heegaard (diagrams de Heegaard)
Il a introduit les outils de la cobordisme, l’homologie, le groupefundamental, l’idee de homeomorphisme . . . .
![Page 21: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/21.jpg)
Selon Poincare, une variete est:
1) comme l’ensemble des pointes reguliers qui satisfient une systemedes egalites et inegalites des fonctions differentielles de n variables
2) comme une chaine des domaines parametrizes par fonctionsanalytique (de maniere de la continuation analytique)
3) comme une somme des polyedres qui satisfait particuliersconditions
4) comme les methodes de Heegaard (diagrams de Heegaard)
Il a introduit les outils de la cobordisme, l’homologie, le groupefundamental, l’idee de homeomorphisme . . . .
![Page 22: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/22.jpg)
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A Blaricum, Alexandroff , Brouwer, et Urysohn
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Witold Hurewicz (1904–1956) et Hans Freudenthal (1905–1990)
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Emmy Noether Helmut Kneser et Heinz Hopf
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Leopold Vietoris (1891–2002)
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Pavel S. Alexandroff (1896–1982) et Heinz Hopf (1894–1971)
![Page 29: A History of Early Algebraic Topology · A History of Early Algebraic Topology John McCleary, Vassar College June 6, 2013](https://reader034.vdocuments.mx/reader034/viewer/2022042208/5eac2721e06c520a661f18fd/html5/thumbnails/29.jpg)
Eduard Cech (1893–1960)
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W. Hurewicz, Koninklijke Akademie van Wetenschappen, 38(1935),112–119; 38(1935), 521–528; 39(1936), 117–126; 39(1936),215–224. Tous communiques par L. E. J. Brouwer.
Beitrage zur Topologie der Deformationen. I . HoherdimensionaleHomotopiegruppen
Beitrage zur Topologie der Deformationen. II . Homotopie- undHomologiegruppen
Beitrage zur Topologie der Deformationen, III . Klassen undHomologietypen von Abbildungen
Beitrage zur Topologie der Deformationen, IV . Aspharische Raume
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Une photo des participants a le1935 Moscou Conference de la Topologie