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 . 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 is a cohomology theory on the space of a simplicial complex which is locally constant on every open simplex of there is a spectral sequence converging to whose -term is the usual simplicial cohomology of with coefficients in various stacks on defined by . This generalizes some known spectral sequences.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1992-1024777-X

Article copyright:
© Copyright 1992
American Mathematical Society