On the finiteness of the classifying space for the family of virtually cyclic subgroups

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups, that they do not admit a finite model for this classifying space unless they are virtually cyclic. This settles a conjecture due to Juan-Pineda and Leary for these classes of groups.Comment: Minor changes, to appear in Groups, Geometry, and Dynamic

Strukturelle und kulturelle Grundlagen des Politischen in Ostmitteleuropa im 20. Jahrhundert

Structural and Cultural Foundations of the Political Sphere in East Central Europe in the 20th Century The cultural turn in political history challenges established notions of East Central Europe. Yet, a survey of recent studies shows that the concept of East Central Europe is still provides valid insights into specific traits of the regions within a European context. The article explores the national connotations of statehood since the late nineteenth century. It argues that not so much unsolved minority problems, but rather the need to develop coherent ideas of a national state and a national territory within the majority populations posed the most serious problems in establishing the new political order after 1918. The answer was to link national statehood to farreaching reform projects. The communist regimes took a similar approach in propagating socialist utopia within a national framework. Even today, discourses of national statehood, liberty and civil society reflect specific traditions of the historical experience of East Central Europe

On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups

This thesis mainly deals with finiteness properties of the classifying space for the family of virtually cyclic subgroups. We establish a link between the finiteness of the classifying space and the conjugacy growth invariant of the given group and use this connection to show that the classifying space for virtually cyclic subgroups is not of finite type except in trivial cases if the group is linear or a CAT(0) cube group. We also investigate the class of residually finite groups in this context and along the way come close to a classification of the finite groups which have only two conjugacy classes of maximal cyclic subgroups

Geschichte des Königlich Preussischen Kaiser Franz Garde-Grenadier-Regiments Nr. 2

GESCHICHTE DES KÖNIGLICH PREUSSISCHEN KAISER FRANZ GARDE-GRENADIER-REGIMENTS NR. 2 Geschichte des Königlich Preussischen Kaiser Franz Garde-Grenadier-Regiments Nr. 2 / Puttkamer, Erich von (Public Domain) ( - ) Title page ( - ) Preface ( - ) Contents ([VII]) Einleitung ([1]) Erster Abschnitt. Von der Stiftung bis zum Jahre 1848 ([12]) Zweiter Abschnitt. Der Feldzug in Schleswig 1848 ([24]) Dritter Abschnitt. Friedensperiode von 1849-1866 ([38]) Vierter Abschnitt. Der Feldzug gegen Österreich 1866 ([47]) Fünfter Abschnitt. Friedensperiode von 1866-1870 ([91]) Abbildung: Vergessen wir die treuen Todten nie. Sie fielen, das Schwert in muthiger Hand, mit Gott für König und Vaterland ( - ) Sechster Abschnitt. Der Feldzug gegen Frankreich 1870/71. Die Mobilmachung und der Eisenbahn-Transport ([93]) Siebenter Abschnitt. Schluß ([189]) Achter Abschnitt. Die Fahnen des Regiments ([247]) Neunter Abschnitt. Die Uniform-Veränderungen ([258]) Zehnter Abschnitt. Bei der Garde Landwehr ([262]) Anlage 1. Übersicht der Ausrückestärke des Regiments an den Gefechtstagen der Feldzüge 1866 und 1870/71 [...] ([270]) Table ([270]) Anlage 2. Namentliche Liste aller in den Feldzügen 1848, 1866 und 1870-71 Gefallenen ([271]) Anlage 3. Es haben Dekorationen beim Rigiment erhalten [...] ([279]) Rangliste des Kaiser Franz Garde-Grenadier-Regiments Nr. 2, 1. Juli 1902 ([285]) Imprint ( - ) Karte: Plan 1. Plan des Gefechtsfeldes von Soor am 28. Juni 1866 (Alt-Rognitz und Rudersdorf) ( - ) Karte: Plan 2. Plan des Gefechtsfeldes bei Lipa am 3. Juli 1866 ( - ) Karte: Plan 2a. Stand der beiderseitigen Armeeen am Abend des 2. Juli 1866 ( - ) Karte: Plan 3. Plan des Gefechtsfeldes bei St. Privat ( - ) Karte: Plan 4. Gefechtsfeld bei Sedan am 1. Sept. 1870 ( - ) Karte: Plan 4a. Stellung der Franzosen am Morgen des 1. September 1870 ( - ) Karte: Plan 5. Renvoi ( - ) Karte: Plan 6. Cernierungs-Abschnitt vor Paris ( - ) Karte: Plan 7. Marschkarte zum Feldzug 1866 ( - ) Karte: Plan 8. Die Märsche des Kaiser-Franz-Gde. Gren. Regts. No. 2. in dem Feldzuge 1870/1871 ( - ) Handschriftliche Notiz ( - ) ColorChart ( -

Hierarchically cocompact classifying spaces for mapping class groups of surfaces

We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group Mod ( S ) of any connected oriented compact surface S , possibly with punctures and boundary components and with negative Euler characteristic has a hierarchically cocompact model for the family of virtually cyclic subgroups of dimension at most vcd Mod ( S ) + 1 . When the surface is closed, we prove that this bound is optimal. In particular, this answers a question of Lück for mapping class groups of surfaces