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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sheaves with finitely generated isomorphic stalks and homology manifolds


Authors: Jerzy Dydak and John Walsh
Journal: Proc. Amer. Math. Soc. 103 (1988), 655-660
MSC: Primary 57P05; Secondary 18F20, 54B40
MathSciNet review: 943100
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Abstract: The setting is sheaves of modules over a commutative ring $ L$. It is shown that on completely metrizable spaces certain sheaves having mutually isomorphic finitely generated stalks are locally constant over a dense open subset. This is used to show that a locally compact metrizable space $ X$ that is homologically locally connected with respect to a principal ideal domain $ L$ is a homology manifold over $ L$ provided it has finite cohomological dimension with respect to $ L$ and, for any two points $ x,y \in X$, the modules $ {H_k}(X,X - \{ x\} ;L)$ and $ {H_k}(X,X - \{ y\} ;L)$ are isomorphic and finitely generated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0943100-4
PII: S 0002-9939(1988)0943100-4
Keywords: Homology manifold, sheaf
Article copyright: © Copyright 1988 American Mathematical Society