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Über die Klassen der Sphärenabbildungen I. Große Dimensionen

@article{Freudenthal1938berDK,
  title={{\"U}ber die Klassen der Sph{\"a}renabbildungen I. Gro{\ss}e Dimensionen},
  author={Hans Freudenthal},
  journal={Compositio Mathematica},
  year={1938},
  volume={5},
  pages={299-314}
}
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References

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c(de) sei ein tatsâchlich auftretender Wert der Invariante (d=k+1 gerade)

    Siehe Hopf 1, § 2, 5

      c(g) === 0, @g = 0. 9.1. Für d > k + 1 und gerades d = k + 1 hat man nach 8

        Um das zu zeigen, wâhlen wir Punkte py mit den Brei-fJ (v=1, 2)

          Unwesentlichkeit von g. 9.2. Gibt es ein 1jJ E (d+l.,+2) mit der Invariante -c', so verfahre man so: Man ersetze f (siehe 8.1) durch die kleine Abânderung f1

            * = 2 f = @2g ( f * (Se+1 ) C Sd+l) so einrichten, daB c"(f*)=2C'(f) wird. Da das gerade ist, kônnen wir 9.2 immerhin auf f * = 2f anwenden und auf die Unwesentlichkeit von 2g schliel3en

            • Damit ist Satz

            Z §j) und YÎ.+2 seihen die Urbildkomplexe eines in V2 liegenden, von p § nach p § gerichteten Streckenzuges, und zwar bzw

              Das Vorzeichen e hängt nur von der Dimension ab; siehe a

                Für d > k + 1 ist c = c' = c" -0. -Für gerades d = k + 1 ist b antisymmetrisch 25), also c' + c" = 0; andererseits c

                  Beweis von Satz Il