Connected sum decompositions of high-dimensional manifolds

Abstract

The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. We discuss to what degree such decompositions exist in higher dimensions and we show that in many settings uniqueness fails in higher dimensions.

25 pages, fixed several minor mistakes, final version

References in corpus (3)

• A survey of the foundations of four-manifold theory in the topological category
• Realizing algebraic 2-complexes by cell complexes
• Cancellation for $(G,n)$-complexes and the Swan finiteness obstruction

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• The classification of surfaces via normal curves
• Manifolds with small topological complexity