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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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Article copyright: © Copyright 1992 American Mathematical Society

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