Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

An algorithmic approach to Dold-Puppe complexes

Pages: 301 – 326

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n1.a15

Authors

Bernhard Köck (School of Mathematics, University of Southampton, United Kingdom)

Ramesh Satkurunath (School of Mathematics, University of Southampton, United Kingdom)

Abstract

A Dold-Puppe complex is the image $NFΓ(C.)$ of a chain complex $C$. under the composition of the functors $Γ$, $F$ and $N$, where $Γ$ and $N$ are given by the Dold-Kan correspondence and $F$ is a not necessarily linear functor between two abelian categories. The first half of this paper gives an algorithm that streamlines the calculation of $Γ(C.)$. The second half gives an algorithm that allows the explicit calculation of the Dold-Puppe complex $NFΓ(C.)$ in terms of the cross-effect functors of $F$.

Keywords

Dold-Puppe complex; simplicial module; cross-effect functor

2010 Mathematics Subject Classification

18G10, 18G30

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