Chain complexes and assembly (Q1118858)
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scientific article; zbMATH DE number 4096381
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chain complexes and assembly |
scientific article; zbMATH DE number 4096381 |
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Chain complexes and assembly (English)
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1990
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We investigate the chain homotopy theory of local systems of finite chain complexes of finitely generated free R-modules over a \(\Delta\)-set X, for any commutative ring R. The assembly of such a system is a finite chain complex of finitely generated free \(R[\pi_ 1(X)]\)-modules. Assembly is related to the augmentation map from the Pontryagin ring \(H_*(\Omega X;R)\) of the loop space \(\Omega\) X to \(H_ 0(\Omega X;R)=R[\pi_ 1(X)]\).
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group ring of the fundamental group
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Pontryagin ring of the loop space
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chain homotopy theory of local systems of finite chain complexes
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modules over a Delta-set
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assembly
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