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dc.contributor.authorRahm, Alexander D.
dc.date.accessioned2014-01-31T15:48:21Z
dc.date.available2014-01-31T15:48:21Z
dc.date.issued2014
dc.identifier.citationAlexander D. Rahm (2014) 'Accessing the cohomology of discrete groups above their virtual cohomological dimension'. Journal Of Algebra, [in press]en_US
dc.identifier.urihttp://arxiv.org/abs/1112.4262
dc.identifier.urihttp://hdl.handle.net/10379/4120
dc.descriptionJournal article (in press)en_US
dc.description.abstractWe introduce a method to explicitly determine the Farrell-Tate cohomology of discrete groups. We apply this method to the Coxeter triangle and tetrahedral groups as well as to the Bianchi groups, i.e. PSL_2 over the ring of integers in an imaginary quadratic number field, and to their finite index subgroups. We show that the Farrell-Tate cohomology of the Bianchi groups is completely determined by the numbers of conjugacy classes of finite subgroups. In fact, our access to Farrell-Tate cohomology allows us to detach the information about it from geometric models for the Bianchi groups and to express it only with the group structure. Formulae for the numbers of conjugacy classes of finite subgroups in the Bianchi groups have been determined in a thesis of Kramer, in terms of elementary number-theoretic information on the ring of integers. An evaluation of these formulae for a large number of Bianchi groups is provided numerically in the appendix. Our new insights about the homological torsion allow us to give a conceptual description of the cohomology ring structure of the Bianchi groups.en_US
dc.formatapplication/pdfen_US
dc.language.isoenen_US
dc.relation.ispartofJournal Of Algebraen
dc.subjectDiscrete groupsen_US
dc.subjectBianchi groupsen_US
dc.subjectFarrell-Tate cohomologyen_US
dc.subjectCohomology ring structureen_US
dc.titleAccessing the cohomology of discrete groups above their virtual cohomological dimensionen_US
dc.typeArticleen_US
dc.date.updated2014-01-10T12:29:51Z
dc.description.peer-reviewedpeer-reviewed
dc.contributor.funder|~|IRCSET|~|
dc.internal.rssid5711301
dc.local.contactAlexander Rahm, School Of Maths, Stats &, Applied Maths,, Nui Galway.. Email: alexander.rahm@nuigalway.ie
dc.local.copyrightcheckedYes
dc.local.versionSUBMITTED
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