# Frank Tall: A provisional solution to Nyikos’ manifold problem

14/Jun/2013, 13:30–15:00
Fields institute,Room 210

Speaker: Frank Tall

Title: A provisional solution to Nyikos’ manifold problem

Abstract: Peter Nyikos observed that, although the Long Line is a non-metrizable, hereditarily normal manifold, it is difficult to find such a manifold of dimension $>1$. Indeed the only such examples are constructed with extra set-theorteic hypotheses, e.g. CH. He therefore conjectured in 1981 that it was consistent there were no such higher dimensional manifolds. Assuming results claimed by Todorcevic and by Dow, we can prove this, modulo a supercompact cardinal.. Our proof is mainly topological, deriving the nonexistence of such manifolds from the conjunction of several assertions known to follow from or asserted to follow from PFA(S){S].