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.

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