Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Duality in the homology of 5-manifolds

Pages: 171 – 179

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n1.a9


W.H. Mannan (Department of Mathematics, City University London, United Kingdom)


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.


manifold, Poincaré duality, chain complex

2010 Mathematics Subject Classification

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

Published 6 June 2017