Volume 13 (2009) No. 2
Volume 13 (2009) No. 2 
The Arf-Kervaire Invariant of framed manifolds
Victor P. Snaith
Abstract:
This work surveys classical and recent advances around the existence of exotic differentiable structures on spheres and its connection to stable homotopy theory.
$K$-theory of $S^7/Q_8$ and a counterexample to a result of P.M. Akhmet'ev
Peter S. Landweber
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.