### Upper triangular technology and the Arf-Kervaire invariant, by Victor P. Snaith

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.

Victor P. Snaith <v.snaith@sheffield.ac.uk>