Locally constant cohomology
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- by E. Spanier PDF
- Trans. Amer. Math. Soc. 329 (1992), 607-624 Request permission
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 $H(|K|)$ 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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 607-624
- MSC: Primary 55N10; Secondary 55N40
- DOI: https://doi.org/10.1090/S0002-9947-1992-1024777-X
- MathSciNet review: 1024777