A Homotopy Theoretic Analogue to a Theorem of Wall

2022/10/10 by Sebastian Chenery, Chenery, Sebastian
Mathematics · Social Sciences · #57P10 (Primary) 55P35 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics Education and Teaching Techniques

paper · pdf · doi:10.48550/arxiv.2210.04548

openalex publication_date 2022/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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