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A History of Algebraic and Differential Topology, 1900 - 1960The Various Homology and Cohomology Theories

A History of Algebraic and Differential Topology, 1900 - 1960: The Various Homology and... [After 1925 topologists began to look for an extension of the notion of homology groups, until then restricted to the very special and rather artificial case of cell complexes, that would have meaning for the most general topological spaces possible; several such extensions were proposed. The concept of homology groups was enlarged by taking elements of an arbitrary commutative group as coefficients of chains; the duality theorems of topology were thus put in relation with the duality of commutative groups, at first for finite groups only. But the discovery of Pontrjagin duality for locally compact commutative groups yielded a method of dealing with general discrete or compact commutative groups as coefficients.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A History of Algebraic and Differential Topology, 1900 - 1960The Various Homology and Cohomology Theories

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Publisher
Birkhäuser Boston
Copyright
© Birkhäuser Boston 2009
ISBN
978-0-8176-4906-7
Pages
67 –157
DOI
10.1007/978-0-8176-4907-4_5
Publisher site
See Chapter on Publisher Site

Abstract

[After 1925 topologists began to look for an extension of the notion of homology groups, until then restricted to the very special and rather artificial case of cell complexes, that would have meaning for the most general topological spaces possible; several such extensions were proposed. The concept of homology groups was enlarged by taking elements of an arbitrary commutative group as coefficients of chains; the duality theorems of topology were thus put in relation with the duality of commutative groups, at first for finite groups only. But the discovery of Pontrjagin duality for locally compact commutative groups yielded a method of dealing with general discrete or compact commutative groups as coefficients.]

Published: May 29, 2009

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