Dimension functions for spherical fibrations Cihan Okay, Ergün Yalçin Algebraic and Geometric Topology, 2018 Given a spherical fibration $\\xi$ over the classifying space $BG$ of a finite group we define a dimension function for the $m-$fold fiber join of $\\xi$ where $m$ is some large positive integer. We show that the dimension functions satisfy the Borel-Smith conditions when $m$ is large enough. As an application we prove that there exists no spherical fibration over the classifying space of $\\text{Qd}(p)= (\\mathbb{Z}/p)^2\\rtimes\\text{SL}_2(\\mathbb{Z}/p)$ with $p-$effective Euler class, generalizing the result of \\"Ozg\\"un \\"Unl\\"u about group actions on finite complexes homotopy equivalent to a sphere. We have been informed that this result will also appear in a future paper as a corollary of a previously announced program on homotopy group actions due to Jesper Grodal.
