FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 5, PAGES 99-105

On $SL(3,$R)-actions on $4$-spheres

Sh. Kuroki

Abstract

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We construct a natural, continuous $SL(3,$R)-action on $S4$ which is an extension of the $SO(3)$-action $$y of Uchida. The construction is based on the Kuiper theorem asserting that the quotient space of $$CP(2) by complex conjugation is $S4$. We also give a new proof of the Kuiper theorem.

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Last modified: February 26, 2006