Equivariant homology theories for totally disconnected groups [Elektronische Ressource] / vorgelegt von Juliane Sauer, geb. Jänich

Juliane SauerEquivariant Homology Theoriesfor Totally Disconnected Groups2002Reine MathematikEquivariant Homology Theoriesfor Totally Disconnected GroupsInaugural-Dissertationzur Erlangung des Doktorgradesder Naturwissenschaften im Fachbereich Mathematikder Mathematisch-Naturwissenschaftlichen Fakult atder Westf alischen Wilhelms-Universit at Munstervorgelegt vonJuliane Sauer, geb. J anichaus Regensburg2002Dekan: Prof. Dr. F. NattererErster Gutachter: Prof. Dr. W. Luc kZweiterhter: Prof. Dr. H. HammTag der mundlic hen Prufungen: 20.8./23.8./26.8.2002Tag der Promotion: 26.8.2002Equivariant Homology Theories for TotallyDisconnected GroupsJuliane SauerAbstractThe notion of an equivariant family of spectra corresponds to the notion of anequivariant homology theory as used in [Luc02]. A general principle how to con-struct equivariant families of spectra will be given. This machine can be used tode ne many interesting equivariant homology theories. The main examples will bealgebraic K- and L-theory for discrete groups and topological K-theory, HochschildHomology, Cyclic Homology and Periodic Homology for totally disconnected, lo-cally compact groups.In the appendix equivariant K-theory (cohomology) for proper actions of totallydisconnected groups will be considered. We will show that in general it cannot bede ned via equivariant vector bundles as for discrete groups, because of the failureof the excision axiom.