A Criterion for Virtual Euler Class One Using Nonvanishing Alexander Polynomials

The paper presents a criterion for the virtual Euler class one conjecture, which posits that any rational point of dual Thurston norm 1 in the second cohomology group of a closed hyperbolic 3-manifold can be realized as the real Euler class of a taut foliation on some finite cover of the manifold. The criterion hinges on the existence of certain nonvanishing Alexander polynomials associated with the manifold.