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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-algebras modelling Poincaré duality spaces.</p>

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Poincaré dualization and Massey products

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Aleksandar Milivojević,
  • Jonas Stelzig,
  • Leopold Zoller

摘要

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 \(A_\infty \) A ∞ -algebras modelling Poincaré duality spaces.