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Factorable Groups and their Homology

dc.contributor.advisorBödigheimer, Carl-Friedrich
dc.contributor.authorVisy, Balázs
dc.date.accessioned2020-04-16T22:20:06Z
dc.date.available2020-04-16T22:20:06Z
dc.date.issued04.07.2011
dc.identifier.urihttps://hdl.handle.net/20.500.11811/4990
dc.description.abstractIn this thesis we introduce the class of factorable groups. These are normed groups together with a norm preserving decemposition (or factorization) of each group element into two factors.
Already the norm alone gives a filtration of the bar resolution and of the bar complex, which we call the norm filtration and we study the spectral sequence associated to the norm filtration.
The main result of the thesis is that for a factorable group the homology of the columns of the E^0-term is concentrated in the top degree. Consequently, the spectral sequence associated to the norm filtration collapses after the E^2-term and the homology of the group G can be computed as the homology of the E^1-term.
Moreover, using the structure of a factorable group G we can find a free resolution of Z over ZG which has fewer generators than the bar resolution, making computations easier.
en
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectalgebraic topology
dc.subjectcohomology of groups
dc.subject.ddc510 Mathematik
dc.titleFactorable Groups and their Homology
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5N-25590
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID2559
ulbbnediss.date.accepted15.04.2011
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeStroppel, Catharina


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