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We shall study smooth SL(m,R)×SL(n,R) actions on Sm+n-1, each of which is an extension of the standard SO(m)×SO(n) action. We shall show such an action is characterized by a smooth R2-action on the circle. Moreover, we shall show there are uncountably many topologically distinct such extensions.

On Smooth SL(m,R)×SL(n,R)-Actions on Sm+n-1*