Cohomology of finite covers
Author:
Allan Calder
Journal:
Trans. Amer. Math. Soc. 218 (1976), 349-352
MSC:
Primary 55B05
DOI:
https://doi.org/10.1090/S0002-9947-1976-0400205-0
MathSciNet review:
0400205
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Abstract: For a finite dimensional CW-complex, X, and $q > 1$, it is shown that the qth Čech cohomology group based on finite open covers of X, $H_f^q(X)$, is naturally isomorphic to ${H^q}(X)$, the qth Čech cohomology of X (i.e. based on locally finite covers), and for reasonable X, ${H^1}(X)$ can be obtained algebraically from $H_f^1(X)$.
- Allan Calder, On the cohomology of $\beta R^{n}$, Quart. J. Math. Oxford Ser. (2) 25 (1974), 385–394. MR 365549, DOI https://doi.org/10.1093/qmath/25.1.385 E. Čech, Théorie générale de l’homologie dans un espace quelconque, Fund. Math. 19 (1932), 149-183.
- C. H. Dowker, Mapping theorems for non-compact spaces, Amer. J. Math. 69 (1947), 200–242. MR 20771, DOI https://doi.org/10.2307/2371848 S. Eilenberg, Transformations continues en circonférence et la topologie du plan, Fund. Math. 26 (1936), 61-112.
- Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey, 1952. MR 0050886 A. G. Kuroš, The theory of groups, 2nd ed., GITTL, Moscow, 1953; English transl., Chelsea, New York, 1955. MR 15, 501; 17, 124.
- C. N. Lee and Frank Raymond, Čech extensions of contravariant functors, Trans. Amer. Math. Soc. 133 (1968), 415–434. MR 234450, DOI https://doi.org/10.1090/S0002-9947-1968-0234450-X
- Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095
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Article copyright:
© Copyright 1976
American Mathematical Society
