MOVING HOMOLOGY CLASSES IN FINITE COVERS OF GRAPHS

Let Y -> X be a finite normal cover of a wedge of n >= 3 circles. We prove that for any nonzero v is an element of H-1(Y; Q) there exists a lift (F) over tilde to Y of a basepoint-preserving homotopy equivalence F : X -> X such that the set of iterates {(F) over tilde (d)(v) : d is an element of Z} subset of H-1(Y ; Q) is infinite. The main achievement of this paper is the use of representation theory to prove the existence of a purely topological object that seems to be inaccessible via topology.