Free loop spaces and equivariant classifying spaces (Q5946714)

For \(\pi\) a discrete group, \(X\) a classifying space for \(\pi\), SO(2) the topological group of rotations of the plane about the origin and \({\mathcal C}_k\) the cyclic subgroup with \(k\) elements, \({\mathcal C}_k\subset \text{SO}(2)\), the author gives a group-theoretic description of the \({\mathcal C}_k\)-equivariant homotopy type of the path components of \(\Lambda X\) (the free loop space). The results of this paper will be used, in a preprint, for counting periodic orbits of identity maps of \(\pi\)-spaces. Thus the author obtains invariants of the algebraic K-theory of the classifying space of a finite group.