Duality in the homology of 5-manifolds

We show that the homological properties of a 5-manifold $M$ with fundamental group $G$ are encapsulated in a $G$-invariant stable form on the dual of the third syzygy of $\mathbb{Z}$. In this notation one may express an even stronger version of Poincaré duality for $M$. However, we find an obstruction to this duality.

Keywords

manifold, Poincaré duality, chain complex

2010 Mathematics Subject Classification

55N45, 55N91, 55U15, 57M60, 57P10

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Published 6 June 2017