Loop Space Decompositions of Connected Sums and Applications to the Vigu\'e-Poirrier Conjecture

Abstract

Recent work of Beben and Theriault on decomposing based loop spaces of highly connected Poincar\'e 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 give new examples supporting a long standing question of rational homotopy theory: the Vigu\'e-Poirrier Conjecture.