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On the Hopf fibration S7 → S4 Over Z

Published online by Cambridge University Press:  22 January 2016

Takashi Ono
Takashi Ono*
Affiliation:
The Johns Hopkins University
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Let K be the classical quaternion field over the field Q of rational numbers with the quaternion units 1, i, j, k, with relations i2 = j2 = − 1, k = ij = −ji. For a quaternion x ∈ K, we write its conjugate, trace and norm by and Nx, respectively. Put

and consider the map h: A → B defined by

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 59 , December 1975 , pp. 59 - 64
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

1) H. Hopf, Über die Abbildungen von Sphären auf Sphären niedrigerer Dimension, Fund. Math. 25 (1935) 427-440.

2) T. Ono, On the Hopf fibration over Z, Nagoya Math. J. Vol. 56 (1975), 201-207, T. Ono. Quadratic fields and Hopf fibrations (to appear).

3) Yu V. Linnik, Quaternions and Cayley numbers. Some applications of quaternion arithmetic. (Russian), Uspehi Mat. Nauk, IV, 5(33), (1949) 49-98.