A Homotopy Theoretic Analogue to a Theorem of Wall

Abstract

It is a well-known result of C.T.C. Wall's that one may decompose a simply connected 6-manifold as a connected sum of two simpler manifolds. Recent work of Beben and Theriault on decomposing based loop spaces of highly connected Poincaré Duality complexes has yielded new methods for analysing the homotopy theory of manifolds. In this paper we will expand upon these methods, which we will then apply to prove a higher dimensional homotopy theoretic analogue to Wall's Theorem.

19 pages, comments welcome. Newer versions of parts of Sections 2 and 3 are now contained in arXiv:2304.12726 [math.AT]