Chain complexes and assembly
type: Item
instance of: scholarly article
title: Chain complexes and assembly
zbMATH Open document ID: 0669.55010
DOI: 10.1007/BF02570866
author: Andrew Ranicki
author: Michael S. Weiss
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183763
review text: 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 \(H_ 0(\Omega X;R)=R[\pi_ 1(X)]\).
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 57S99
zbMATH DE Number: 4096381
zbMATH Keywords: group ring of the fundamental group
zbMATH Keywords: Pontryagin ring of the loop space
zbMATH Keywords: chain homotopy theory of local systems of finite chain complexes
zbMATH Keywords: modules over a Delta-set
zbMATH Keywords: assembly
MaRDI profile type: Publication
cites work: Q4067782
cites work: Q3320507
cites work: Homotopy limits, completions and localizations
cites work: Geometric Groups and Whitehead Torsion
cites work: Q3830226
cites work: Homology and fibrations I: Coalgebras, cotensor product and its derived functors
cites work: On Products of Complexes
cites work: Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
cites work: Transformation groups and algebraic \(K\)-theory
cites work: Q3924852
cites work: The algebraic theory of finiteness obstruction.
cites work: Δ-SETS I: HOMOTOPY THEORY
description: scientific article; zbMATH DE number 4096381