Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Photographs Read chapter Read first chapter

2017 | OriginalPaper | Chapter

[121] On the Early History of the Periodicity Theorem

Author : Loring W. Tu

Published in: Raoul Bott: Collected Papers

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Excerpt

This paper will be concerned with the period 1949 to 1959 and will, on the whole, be an account of Marston Morses work of the 1920’s, and bow naturally its reinterpretation in the language of the 40’s leads to the periodicity theorem of the homotopy groups of the Classical Stable Groups. I hope to convince you that from that perspective the periodicity theorem is simply an extension of the Freudenthal Suspension Theorem, albeit a quite miraculous one. My paper will therefore also be more personal than is possibly appropriate in this forum, but I find the attempt to play the historian on a larger than personal level much too daunting to undertake, even though, from previous experience, I am also well aware of the perils posed to personal reminiscence by the highly selective nature of our memories. Nevertheless, I hope that this account will be of some use. But please remember, that a ll I can really p romise you here, is how the past appears to me now, some 50 years later. …

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter [120] Surjectivity for Hamiltonian Loop Group Spaces
next chapter [20] In Memoriam Sumner B. Myers 1910–1955
Literature
R. Bott, An Application of the Morse Theory to the Topology of Lie-Groups, Bull. Soc. Math. France, 84, 255-281,1956.MathSciNetMATH
R. Bott and H. Samelson, Applications of the Theory of Morse to Symmetric Spaces, Amer. Jour. of Math., 80 , 964-1024, 1958.MathSciNetCrossRef
H. Freudenthal, Über die Klassen von Sphären Abbildtmgen, Comp. Math., 5 , 299-314, 1937.
M. Morse, Calculus of Variations in the Large, Coll. Pub. Amer. Math. Soc. Coll. Publ., no. 18, P rovidence, Rl, 1934.
H. Seifert and W. Threlfall, Variations Rechnung in Crossen, Te ubner, 1938.
E. Stiefel, Üeber Eine Beziehung zwischen geschlossenen Lieschen und discontinuierlichen Bewegsgruppeuklidischer Räume und ihre Anwendung auf die Aufziihlung der einfachen Lischen Gruppen, Com. Math. Helv., 14 , 350, 1942.CrossRef
Metadata
Title
[121] On the Early History of the Periodicity Theorem
Author
Loring W. Tu
Copyright Year
2017
Book
Raoul Bott: Collected Papers

Print ISBN: 978-3-319-51779-7

Electronic ISBN: 978-3-319-51781-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-51781-0_44

Premium Partner

    Image Credits