Sheaves with finitely generated isomorphic stalks and homology manifolds
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- by Jerzy Dydak and John Walsh PDF
- Proc. Amer. Math. Soc. 103 (1988), 655-660 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 655-660
- MSC: Primary 57P05; Secondary 18F20, 54B40
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943100-4
- MathSciNet review: 943100