This volume contains articles written by the invited speakers and workshop participants from the conference on 'Crystallographic Groups and Their Generalizations', held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.
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978-0-8218-2001-8 (9780821820018)
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Schweitzer Klassifikation
Tores affines by Y. Benoist On structures preserved by idempotent transformations of groups and homotopy types by C. Casacuberta Affine Schottky groups and crooked tilings by V. Charette and W. M. Goldman Polynomial structures on polycyclic groups: Recent developments by K. Dekimpe Problems on the geometry of finitely generated solvable groups by B. Farb and L. Mosher Flat Lorentz 3-manifolds and cocompact Fuchsian groups by W. M. Goldman and G. A. Margulis Varieties of discontinuous groups by O. Baues Affine cohomology classes for filiform Lie algebras by D. Burde Hyperbolic automorphisms for groups in $\mathcal{T}(4,2)$ by C. Cassidy, N. Kennedy, and D. Scevenels Varietes projectives a holonomie dans le groupe $\mathrm{Aff}^{+}({\mathf R})$ by S. Dupont Classification of homogeneous complex affinely flat surfaces with compact quotients and applications to complex projective structures by Y. Kamishima On the fundamental groups of compact complete quaternionic affinely flat 2-manifolds by Y. Kamishima and T. Udono An obstruction to the existence of Anosov diffeomorphisms on infra-nilmanifolds by W. Malfait Genus and localization of virtually nilpotent groups by N. O'Sullivan Immeubles affines: construction par les normes et etude des isometries by A. Parreau Isoclinic spheres and flat homogeneous pseudo-Riemannian manifolds by J. A. Wolf.
