Title: Upper triangular technology and the Arf-Kervaire invariant

Author: Victor Snaith

address: Faculty of Mathematical Studies, University of Southampton,
Southampton SO17 1BJ, England

e-address: vps@maths.soton.ac.uk

      Abstract.  This paper introduces the upper triangular technology
      (UTT) into classical homotopy theory. This is a new and easy to
      use method to calculate the effect of the left unit map in 2-adic
      connective K-theory; the map which is the basis for operations in
      bu-theory. By way of application, UTT is used to give a new, very
      simple proof of a conjecture of Barratt- Jones-Mahowald, which
      rephrases K-theoretically the existence of framed manifolds of
      Arf-Kervaire invariant one.