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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A one dimensional manifold is of cohomological dimension $ 2$


Author: Satya Deo
Journal: Proc. Amer. Math. Soc. 52 (1975), 445-446
MSC: Primary 55B30; Secondary 57A65
DOI: https://doi.org/10.1090/S0002-9939-1975-0394632-2
MathSciNet review: 0394632
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Abstract: G. Bredon defines the cohomological Dimension of a topological space $ X$ to be the supremum of all cohomological $ \phi $-dimensions of $ X$, where $ \phi $ varies over the entire families of supports on $ X$. He has proved that if $ X$ is a topological $ n$-manifold then the cohomological Dimension of $ X$ is $ n$ or $ n + 1$. He was not able to decide which one it is, even for a space as simple as the real line. The objective of this paper is to solve his problem for $ n = 1$. In particular, we have shown that the cohomological Dimension of the real line is $ 2$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0394632-2
Keywords: Sheaves, sections and serrations of sheaves, extent of a family of supports, paracompactifying family of supports, manifolds and dimension of a topological space
Article copyright: © Copyright 1975 American Mathematical Society