Virtual fibers in hyperbolic 3-manifolds (Q1187118)

An immersed surface, \(S\), in a 3-manifold \(M\) is called a ``virtual'' fiber if there is a finite covering \(\widetilde M\) of \(M\) such that \(S\) lifts to \(\widetilde S\) in \(\widetilde M\) and \(\widetilde S\) is homotopic to a fiber in a fiber map of \(\widetilde M\) to \(S^ 1\). The author proves a number of theorems and algorithms relating the existence and construction of virtual fibers to various hyperbolic, algebraic, and geometric invariants.