QUILLEN'S WORK ON THE ADAMS CONJECTURE

In the 1960's and 1970's, the Adams Conjecture g- ured prominently both in homotopy theory and in geometric topol- ogy. Quillen sketched one way to attack the conjecture and then proved it with an entirely dierent line of argument. Both of his approaches led to spectacular and beautiful new mathematics. 1. Background on the Adams Conjecture For a nite CW -complex X, let KO(X) be the Grothendieck group of nite-dimensional real vector bundles over X, and J(X) the quo- tient of KO(X) by the subgroup generated by dierences , where and are vector bundles whose associated sphere bundles are