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.