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

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

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68 pages
English
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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.

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Publié le 01 janvier 2006
Nombre de lectures 33
Langue English

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MathematikMathematikM?nsterOnFtheeiermannClassifyingMathematiscSpaceestf?liscfoonr2006theInformatikFhaftlicamiderlyWilhelms-UnivoforgelegtVirtuallyhaelCyclicNetterSubgroupshInauguraldissertationundzurderErlangungh-NaturwissenscdeshenDoktorgradesakult?tderWNaturwissenschenhaftenersit?timvFvacMichWbausereicagDekJanan:JanProf.ArthDr.ndlicJoacaghimPDCunBartelstzmErsterPr?fung:Gutac2007hPromotion:ter:2007Prof.Dr.Dr.urWToderl?fgahenng24.L?cuarkTZwdereiter31.Gutacuarhter:G E (G)F
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G CW F
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G\EG = BG
EG cd (G) G
Z
cd (G) = 2Z
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E (G)Fin
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K
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E (G) E (G)Fin VCyc
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forndclassifyingexplicitymodelsdelshapterwhicThesehcareonsmalltheinearsomeoutsense.yFaorrinstanace,pro-ifofoftenmisBaum-ConnesthConneseandfamilyofwhiccomputehtheoriesconsistswillonlyedofthetheforeeIntrivialvirtuallysubgroup,ofthenwithaThismohdelalsoforbistheiteer,ulationevoutwgroupoarrell-JonesH-t.respcanatbandeequivcfharacterizedrstupintowalenin-homotopwillymoeqauivgalencesubgroupsaswillbaeincgthat,aisfreedelequivgiv-delyleads-homotophomology-complexofwhicblyhonisgroup.non-equive.ariantotlygroupconiso-tractible.theThtheesethespaces,conjectureastopwofelltheasthetheirconjecturequotienalgebraictsctarepdelselymopredictomawet-groupsyaluating,thathevremeneInbhapter,eenestudieddforotherawilllongon.time.eAwwsomeell-knotionswnelstheoremlofisEilenalbthergfandfamilyGaneawstatessucthatdelthelominimalThedimensionisofobservasomemoroups,delossibleforaantothatfromequalsmothethecohomologicalAdimensionondenitionathisrelativfromsviousdirectobsourceofarrell-Jonesisbexceptbpdimensionossiblydelsifaithaandlastexists,devysexplanationaofalwanddelFwhenconjectures.theseeminimalspacestodinimensionformmighoftBaum-bisomorphismeabthree.theSimilarlyological,-theoryforreducedthe-homotopfamily-algebrasmoinaFofisomorphismallabnitethesubgroupsinofandh-theory,grouquestionsrings,onectivthe.tconjecturesyptheoneofymothesedels-forjsucbatevthcertainwnarianshohomologyeatbacanoIttionedhaspaces.vtheecbthiseenbcloselyexplainedinmorevetailestigatedmongbthingsyemanneylaterauthThen,orsth(seenext[L?c05]hapter,foreareviewsurvofey),construc-andofindnfoumerousobsituationsterminamojustdelsbforde.intowielongmobforupsogroofarise.inparticular,aenat-constructuralhgeometricalmowifaisycally.cyclic.Inthirdthishapterthesis,basedwtheeationfoforcusclassesongtheitproblempoftoconstructingduceexplicitmoyfordesirableectrespamenablespaceforaisotropenwhosedel-complexesclassifying-forofmo,.wherenotcategorylyistothecomputationfamilytheofeallgroupvirtuallywhiccyclicaresusummandsbgroups:thethisofcaseFdoassemesmap,notutseemyieldstooundsbtheethatvoeryforwdiscreteelleunderstocanovd.TheOnecreasoniswhotedyanitofisrelationinamenabletereactionssthetingandtoarrell-JonesstudymorphismtheseWclassifyingwillspacesthatisclassifyingthatLettheyPrefaceappmoarediiielsG F

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