5 papers
Local Inertness of Poincaré duality complexes
Samik Basu, Sebastian Chenery, Ruizhi Huang +2
We prove that, under certain homological conditions, the attaching map of the top cell of a Poincaré duality complex is inert when localised away from a finite set of primes. This…
Homotopy of Simply Connected Complexes with a Spherical Pair
Ruizhi Huang
We establish a loop space decomposition for certain -complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of…
An Almost Flat Spin Manifold Bounds
Fei Han, Ruizhi Huang, Weiping Zhang
We prove that every almost flat spin^ manifold bounds a compact orientable manifold, thereby settling, in the spin^ case, a long-standing conjecture of Farrell--Zdravkovska a…
Local hyperbolicity, inert maps and Moore's conjecture
Ruizhi Huang
We show that the base space of a homotopy cofibration is locally hyperbolic under various conditions. In particular, if these manifolds admit a rationally elliptic closure, then al…
Comparison techniques on inert top cell attachments
Ruizhi Huang
We establish various criteria for the inertness of the top cell attachments of Poincaré duality complexes through nonzero degree maps, algebraic intersection theory and various typ…