[121] On the Early History of the Periodicity Theorem

  • Loring W. Tu
Part of the Contemporary Mathematicians book series (CM)

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.

Prom this...


  1. R. Bott, An Application of the Morse Theory to the Topology of Lie-Groups, Bull. Soc. Math. France, 84, 255-281,1956.MathSciNetzbMATHGoogle Scholar
  2. R. Bott and H. Samelson, Applications of the Theory of Morse to Symmetric Spaces, Amer. Jour. of Math., 80 , 964-1024, 1958.MathSciNetCrossRefGoogle Scholar
  3. H. Freudenthal, Über die Klassen von Sphären Abbildtmgen, Comp. Math., 5 , 299-314, 1937.Google Scholar
  4. M. Morse, Calculus of Variations in the Large, Coll. Pub. Amer. Math. Soc. Coll. Publ., no. 18, P rovidence, Rl, 1934.Google Scholar
  5. H. Seifert and W. Threlfall, Variations Rechnung in Crossen, Te ubner, 1938.Google Scholar
  6. J. P. Serre, Homologie Singuliere des Espaces Fibrés, Ann. Math., 54, 425, 1951.MathSciNetCrossRefGoogle Scholar
  7. 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.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Loring W. Tu
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

Personalised recommendations