Dold-Puppe complexes and the derived functors of the third symmetric power functor

Abstract

For a chain complex C. a Dold-Puppe complex is a complex of the form NFT(C), i.e. the image of C. under the composition of the functors F, F and N; here F and N are the functors given by the Dold-Kan corre- spondence and F is a not-necessarily linear functor between two abelian categories. When C. is a projective resolution of a module the ith homology of this Dold-Puppe complex is the ith derived functor of the functor F. The definition of F is quite abstract and combinatorial. The first half of the first chapter of this thesis gives an algorithm that streamlines the calculation of F(C.). The second half of the first chapter gives algorithms that allow the explicit calculation of the Dold-Puppe complex in terms The second chapter produces a partial proof of Kock's predictions of the derived functors of the third symmetric power functor Sym3. This is achieved by comparing certain cross-effect modules of the predictions and of the derived functors.

More information

Identifiers

Catalogue record

Export record

ASCII CitationAtomBibTeXData Cite XMLDublin CoreDublin CoreEP3 XMLEndNoteHTML CitationHTML CitationHTML ListJSONMETSMODSMPEG-21 DIDLOpenURL ContextObjectOpenURL ContextObject in SpanRDF+N-TriplesRDF+N3RDF+XMLRIOXX2 XMLReferReference ManagerSimple Metadata