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Poincaré duality and commutative differential graded algebras

Pascal Lambrechts, Don Stanley (2008)

Annales scientifiques de l'École Normale Supérieure

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.

Precobalanced and cobalanced sequences of modules over domains

Anthony Giovannitti, H. Pat Goeters (2007)

Mathematica Bohemica

The class of pure submodules ( 𝒫 ) and torsion-free images ( ) of finite direct sums of submodules of the quotient field of an integral domain were first investigated by M. C. R. Butler for the ring of integers (1965). In this case 𝒫 = and short exact sequences of such modules are both prebalanced and precobalanced. This does not hold for integral domains in general. In this paper the notion of precobalanced sequences of modules is further investigated. It is shown that as in the case for abelian groups...

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