University of Manchester on research and international reputation, whereas national rankings are largely based on entry standards, graduate prospects and student satisfaction with teaching at the university. In fact, a recent poll voted Manchester as the third "most underrated university in the UK" More students apply to Manchester than to any other university in the country, with more than 55,000 applications for undergraduate courses in 2014 resulting in 6.5 applicants for every available place. Manchester had the 17th highest average entry qualification for undergraduates of any UK university in 2015, with new students averaging 431 UCAS points, equivalent to just above A*AAb or
Virtually fibered conjecture fact, given that the geometrization conjecture is now settled, the only case needed to be proven for the virtually fibered conjecture is that of hyperbolic 3-manifolds. The original interest in the virtually fibered conjecture (as well as its weaker cousins, such as the virtually Haken conjecture) stemmed from the fact that any of these conjectures, combined with Thurston's hyperbolization theorem, would imply the geometrization conjecture. However, in practice all known attacks on the "virtual" conjecture take geometrization as a hypothesis, and rely on the geometric and group-theoretic properties of hyperbolic 3-manifolds. The virtually fibered conjecture was not actually conjectured by