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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Locally constant cohomology


Author: E. Spanier
Journal: Trans. Amer. Math. Soc. 329 (1992), 607-624
MSC: Primary 55N10; Secondary 55N40
MathSciNet review: 1024777
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Abstract: In this paper we study locally constant cohomology theories on a space $ X$. We prove that for cohomology theories on a category of paracompact spaces the homotopy axiom of Eilenberg-Steenrod is a consequence of the other Eilenberg-Steenrod axioms together with continuity and either additivity or weak additivity. We also prove that if $ H$ is a cohomology theory on the space of a simplicial complex $ K$ which is locally constant on every open simplex of $ K$ there is a spectral sequence converging to $ H(\vert K\vert)$ whose $ {E_2}$-term is the usual simplicial cohomology of $ K$ with coefficients in various stacks on $ K$ defined by $ H$. This generalizes some known spectral sequences.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1024777-X
PII: S 0002-9947(1992)1024777-X
Article copyright: © Copyright 1992 American Mathematical Society