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Simplicial and Homotopical Cohomology of Polyhedra

Published online by Cambridge University Press:  20 November 2018

Emil Stamm
Emil Stamm*
Affiliation:
University of Toronto
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It is well known that, on the category of finite polyhedra, any two cohomology theories, satisfying the Eilenberg-Steenrod axioms, are isomorphic. Examples of such theories are simplicial cohomology and homotopical cohomology (the latter is defined by means of homotopy classes of maps into Eilenberg-MacLane spaces). In the case of polyhedra, using triple sequences and spectral sequences, one obtains a deep insight into the relationship between general cohomology theories (without the dimension axiom) and ordinary simplicial cohomology (1, p. 66). As a corollary the abovementioned uniqueness of cohomology theories satisfying the dimension axiom is obtained.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 413 - 423
Copyright
Copyright © Canadian Mathematical Society 1966

References

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