SMF

The rigidity of Poincaré duality algebras and ification of homotopy types of manifolds

The rigidity of Poincaré duality algebras and ification of homotopy types of manifolds

Martin MARKL
  • Année : 1990
  • Tome : 191
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 57P10, 13D10, 55P15
  • Pages : 221-237
  • DOI : 10.24033/ast.55

We prove that Poincaré duality algebras are characterized by a certain rigidity property. As a consequence of this fact, we show that the $k$-isomorphism of a Poincaré duality algebra $H^*$ of top dimension $n$ is uniquely determined by the factor $H^*/H^n$, provided that $k$ is algebraically closed. Using this and usual methods of descent theory, we obtain a description of the set of $k$-isomorphism es of Poincaré duality algebras with the same given isomorphism of $H^*/H^n$, for any field $k$ of characteristic zero. These results are then applied to the study of homotopy types of simply connected Poincaré duality spaces.

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