Poincaré dualization and Massey products

Abstract

We study the rational homotopy theoretic and geometric properties of a construction which extends any cohomologically connected, finite type cdga to one satisfying cohomological Poincaré duality. Using this construction we show that non-trivial quadruple Massey products can pull back trivially under non-zero degree maps of Poincaré duality spaces, unlike the case of triple Massey products as studied by Taylor. We also show that a non-zero degree map between formal rational Poincaré duality spaces need not be formal. Our consideration of Massey products naturally ties in with cyclic $A_{\infty }$-algebras modelling Poincaré duality spaces.

arXiv commentTo appear in JHRS, comments always welcome