Abstract
In [ l ] Browder and Livesay defined an invariant a(Tt 2 ) £ 8 Z of a free differentiate involution T of a homotopy (4&+3)-sphere 2 , k>0. I t is the precise obstruction to finding an invariant (4&+2)sphere of the involution. In [5] and [o] Medrano showed how to construct free involutions with arbitrary Browder-Livesay invariant on some homotopy (4&+3) -spheres and hence that there exist infinitely many distinct involutions. In this note we investigate the homotopy spheres constructed by Medrano. We are indebted to W. Browder for helpful criticism of an earlier version of this paper. Let ju generate bPu+h [2] denote the representative of S in O4&+3 and y be an arbitrary element of du+z*
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