Poincaré Duality Spaces
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A Poincaré duality space of dimension $d$ consists of a space $X$ together a pair $(\cal L,[X])$ in which $\cal L$ is a bundle of local coefficients on $X$ which is free abelian of rank one and $[X] \in H_d(X;\cal L)$ sastifies $$ \cap [X] : H^*(X;M) \to H_{d-*}(X;M \otimes \cal L) $$ is an isomorphism. Here, $M$ is allowed to range over all local coefficient bundles on $X$. | A Poincaré duality space of dimension $d$ consists of a space $X$ together a pair $(\cal L,[X])$ in which $\cal L$ is a bundle of local coefficients on $X$ which is free abelian of rank one and $[X] \in H_d(X;\cal L)$ sastifies $$ \cap [X] : H^*(X;M) \to H_{d-*}(X;M \otimes \cal L) $$ is an isomorphism. Here, $M$ is allowed to range over all local coefficient bundles on $X$. | ||
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1 Introduction
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together a pair Tex syntax errorin which
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which is free abelian of rank one and Tex syntax errorsastifies
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is allowed to range over all local coefficient bundles on .
