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Proceedings of the American Mathematical Society

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Applications of homotopy in sheaf theory


Author: James M. Parks
Journal: Proc. Amer. Math. Soc. 34 (1972), 601-604
MSC: Primary 55B30
DOI: https://doi.org/10.1090/S0002-9939-1972-0451233-2
MathSciNet review: 0451233
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Abstract: Various mapping theorems for sheaf cohomology are obtained, where coefficients are in locally constant sheaves or limits of locally constant sheaves. Applications are made to the continuity of sheaf cohomology on homotopy-systems. A generalization of the Alexander-Čech cohomology continuity theorem is an immediate consequence.


References [Enhancements On Off] (What's this?)

  • [1] D. G. Bourgin, Modern algebraic topology, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0160201
  • [2] Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221500
  • [3] Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey, 1952. MR 0050886
  • [4] James M. Parks, Homotopy-systems, H-spaces and sheaf cohomology, Ph.D. Dissertation, University of Houston, Houston, Texas, 1971.
  • [5] Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0451233-2
Keywords: Locally constant sheaves, sheaf theory, limits of sheaves, continuity of sheaf cohomology, homotopy-systems, mapping theorems in sheaf cohomology
Article copyright: © Copyright 1972 American Mathematical Society