$K$-theory of $S^7/Q_8$ and a counterexample to a result of P.M. Akhmet'ev

Abstract

A simple counterexample is presented to a proposition which is used in the arguments given by P. M. Akhmet'ev in his work on the Hopf invariant and Kervaire invariant. The counterexample makes use of the $K$-theory of the quotient of the 7-sphere by the quaternion group of order 8.

Version published in Morfismos Vol. 13, No. 2, 2009, pp. 55-60

References in corpus (2)

• Geometric approach towards stable homotopy groups of spheres. The Hopf invariant
• Geometric approach towards stable homotopy groups of spheres. The Kervaire invariant II