# Cohomology Theories

@inproceedings{Brown2010CohomologyT,
title={Cohomology Theories},
author={Edgar H. Brown},
year={2010}
}
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121 Citations
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Fibre bundles, an integral part of differential geometry, are also important to physics. This text, a succint introduction to fibre bundles, includes such topics as differentiable manifolds and

### f1 Ky go and ?1 play the role of Zf 1,f2, Sn, C0 and C1. Suppose ?i: go -(S is a covariant functor. Axiom h*. If f and g: X -Y are homotopic, =(f) ==(g)

• f1 Ky go and ?1 play the role of Zf 1,f2, Sn, C0 and C1. Suppose ?i: go -(S is a covariant functor. Axiom h*. If f and g: X -Y are homotopic, =(f) ==(g)
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### First, it is difficult to recover =1(X) from [X, ]; and second, annihilating cohomology classes is more difficult than annihilating homotopy classes

• First, it is difficult to recover =1(X) from [X, ]; and second, annihilating cohomology classes is more difficult than annihilating homotopy classes

### If ir satisfies h*, e* and c*, then there is an Xe 1?, unique up to homotopy type, and a natural equivalence

• BRANDEIS UNIVERSITY BIBLIOGRAPHY

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• This content downloaded on Thu, 7 Mar 2013 22:50:16 PM All use subject to JSTOR Terms and Conditions

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### and, by the exact sequence of the triple (SX, X-, x), Hq+l(SX, X-)Hq+l(SX, x0). Clearly all these isomorphisms are natural. Let p be the base point of Sn

• By excision, Hq(p) Hq(SO