Volodin space

In mathematics, more specifically in topology, the Volodin space of a ring R is a subspace of the classifying space given by
where is the subgroup of upper triangular matrices with 1's on the diagonal and a permutation matrix thought of as an element in [general linear group|] and acting by conjugation. The space is acyclic and the fundamental group is the Steinberg group of R. In fact, showed that X yields a model for Quillen's plus-construction in algebraic K-theory.

Application

An analogue of Volodin's space where GL is replaced by the Lie algebra was used by to prove that, after tensoring with Q, relative K-theory K, for a nilpotent ideal I, is isomorphic to relative cyclic homology HC. This theorem was a pioneering result in the area of trace methods.