Volumen 13 (2009) No. 2

The Arf-Kervaire Invariant of framed manifolds

Victor P. Snaith

Resumen:

This work surveys classical and recent advances around the existence of exotic differentiable structures on spheres and its connection to stable homotopy theory.

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

Peter S. Landweber

Resumen:

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.

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