2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124143This paper studies the homotopy type of the moduli space of compact n-manifold thickenings of a finite complex. The main result computes the homotopy fibers of the stabilization map from n-thickenings to (n+1)-thickenings in a wide range. In particular, we obtain an EHP-type sequence for thickenings extending work of C.T.C. Wall.Algebraic TopologyGeometric Topology57R19; 55N45text