the first definition of higher "k"-theory to be widely accepted was daniel quillen's. as part of quillen's work on the adams conjecture in topology, he had constructed maps from the classifying spaces "bgl"(f) to the homotopy fiber of , where ψ is the "q"th adams operation acting on the classifying space "bu". this map is acyclic, and after modifying "bgl"(f) slightly to produce a new space "bgl"(f), the map became a homotopy equivalence. this modification was called the plus construction. the adams operations had been known to be related to chern classes and to "k"-theory since the work of grothendieck, and so quillen was led to define the "k"-theory of "r" as the homotopy groups of "bgl"("r"). not only did this recover "k" and "k", the relation of "k"-theory to the adams operations allowed quillen to compute the "k"-groups of finite fields.