On the classifying space for the family of virtually cyclic subgroups [Elektronische Ressource] / vorgelegt von Michael Weiermann

MathematikMathematikM?nsterOnFtheeiermannClassifyingMathematiscSpaceestf?liscfoonr2006theInformatikFhaftlicamiderlyWilhelms-UnivoforgelegtVirtuallyhaelCyclicNetterSubgroupshInauguraldissertationundzurderErlangungh-NaturwissenscdeshenDoktorgradesakult?tderWNaturwissenschenhaftenersit?timvFvacMichWbausereicagDekJanan:JanProf.ArthDr.ndlicJoacaghimPDCunBartelstzmErsterPr?fung:Gutac2007hPromotion:ter:2007Prof.Dr.Dr.urWToderl?fgahenng24.L?cuarkTZwdereiter31.Gutacuarhter:G E (G)FF G GG CW FGTrE (G) = EG GTrG CWG\EG = BGEG cd (G) GZcd (G) = 2ZFin GE (G) = EGFinE (G)FinE (G) VCycVCycK∗CK LK LE (G) E (G)Fin VCycGE (G) E (G)FinVCycE (G)VCycE (G)FforndclassifyingexplicitymodelsdelshapterwhicThesehcareonsmalltheinearsomeoutsense.yFaorrinstanace,pro-ifofoftenmisBaum-ConnesthConneseandfamilyofwhiccomputehtheoriesconsistswillonlyedofthetheforeeIntrivialvirtuallysubgroup,ofthenwithaThismohdelalsoforbistheiteer,ulationevoutwgroupoarrell-JonesH-t.respcanatbandeequivcfharacterizedrstupintowalenin-homotopwillymoeqauivgalencesubgroupsaswillbaeincgthat,aisfreedelequivgiv-delyleads-homotophomology-complexofwhicblyhonisgroup.non-equive.ariantotlygroupconiso-tractible.theThtheesethespaces,conjectureastopwofelltheasthetheirconjecturequotienalgebraictsctarepdelselymopredictomawet-groupsyaluating,thathevremeneInbhapter,eenestudieddforotherawilllongon.