TL;DR
This paper explores the homological properties of 5-manifolds with a focus on duality, revealing a G-invariant stable form and identifying an obstruction to a stronger form of Poincare duality.
Contribution
It introduces a G-invariant stable form on the dual of the third syzygy of Z that encapsulates homological properties and discusses an obstruction to an enhanced duality in 5-manifolds.
Findings
Homological properties are encapsulated in a G-invariant stable form.
An enhanced version of Poincare duality is proposed.
An obstruction to this stronger duality is identified.
Abstract
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 Z. In this notation one may express an even stronger version of Poincare duality for M. However we find an obstruction to this duality.
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