dc.contributor.author Nguyen, The Cuong dc.date.accessioned 2017-09-07T08:13:35Z dc.date.available 2017-09-07T08:13:35Z dc.date.issued 2017-07-04 dc.identifier.uri http://publications.mfo.de/handle/mfo/1305 dc.description OWLF 2016 en_US dc.description.abstract Resolving objects in an abelian category by injective (projective) resolutions is a fundamental problem in mathematics, and this article aims at introducing a particular solution called “Pseudo-hyperresolutions”. This method originates in the category of unstable modules to study the minimal resolution of the reduced singular cohomology of spheres. In particular, for all integers $n \geq 0$, we can describe a large range of the minimal injective resolution of the sphere $S^n$ based on the Bockstein operation of the Steenrod algebra. Moreover, many classical constructions in algebraic topology, such as the algebraic EHP sequence or the Lambda algebra can be recovered using the Pseudo-hyperresolution method. A particular connection between spheres and the projective spaces is also established. Despite its origin, Pseudo-hyperresolutions generalize to all abelian categories. In particular, many classical construction of injective resolutions of strict polynomial functors can be reunified in view of Pseudo-hyperresolutions. As a consequence, we recover the global dimension of the category of homogeneous strict polynomial functors of finite degree as well as the Mac Lane cohomology of finite fields. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2017,17 dc.title The Pseudo-Hyperresolution and Applications en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2017-17 local.scientificprogram OWLF 2016 en_US local.series.id OWP-2017-17 dc.identifier.urn urn:nbn:de:101:1-20170807736 dc.identifier.ppn 1654051098
﻿