Poincaré Duality Spaces
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==Introduction== | ==Introduction== | ||
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− | A Poincaré duality space of dimension $d$ consists of a space $X$ together a pair $(\ | + | A Poincaré duality space of dimension $d$ consists of a space $X$ together a pair $(\mathcal{L},[X])$ in which $\mathcal{L}$ is a bundle of local coefficients on $X$ which is free abelian of rank one and $[X] \in H_d(X;\mathcal {L})$ sastifies |
− | + | $$ \cap [X] : H^*(X;M) \to H_{d-*}(X;M \otimes \mathcal{L})$$ | |
+ | is an isomorphism. Here, $M$ is allowed to range over all local coefficient bundles on $X$. | ||
</wikitex> | </wikitex> | ||
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== References == | == References == | ||
{{#RefList:}} | {{#RefList:}} | ||
[[Category:Theory]] | [[Category:Theory]] |
Revision as of 15:59, 21 March 2011
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1 Introduction
A Poincaré duality space of dimension consists of a space together a pair in which is a bundle of local coefficients on which is free abelian of rank one and sastifies
is an isomorphism. Here, is allowed to range over all local coefficient bundles on .