Locally constant cohomology

Spanier, E.

doi:10.1090/S0002-9947-1992-1024777-X

Locally constant cohomology
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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.

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