An algebraic construction for integral Čech cohomology. (English) Zbl 0859.18013
Let \(X\) be a compact Hausdorff space. The real Čech cohomology of \(X\) may be obtained from a cohomology construction for the algebra of continuous real valued functions on \(X\) [C. E. Watts, Proc. Natl. Acad. Sci. USA 54, 1027–1028 (1965; Zbl 0141.40303)]. In this paper, the author defines a cohomology construction for a pair consisting of a commutative algebra, and a space associated to the algebra, which yields the integral Čech cohomology of \(X\) in a special case.
Reviewer: D.Tanré (Villeneuve d’Ascq)
MSC:
| 18G60 | Other (co)homology theories (MSC2010) |
| 55N05 | Čech types |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 13D03 | (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) |
Citations:
Zbl 0141.40303References:
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| [2] | Godement, R., Theorie des Faisceaus (1958), Herman: Herman Paris |
| [3] | Hofmann, K. H., Representations of algebras by continuous sections, Bull. AMS, 78, 291-373 (1972) · Zbl 0237.16018 |
| [4] | Kitchen, A. T., Algebraic Alexander-Spanier cohomology, (Ph.D. Thesis (1971), University of Rochester) · Zbl 0293.18025 |
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| [7] | Watts, C. E., Alexander-Spanier cohomology and rings of continuous functions, (Proc. Nat. Acad. Sci. U.S.A., 54 (1965)), 1027-1028 · Zbl 0141.40303 |
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