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Crystallographic Groups and Their Generalizations
Edited by: Paul Igodt, Katholieke Universiteit Leuven, Kortrijk, Belgium, Herbert Abels, Universitaet Bielefeld, Germany, Yves Félix, Université Catholique de Louvain, Belgium, and Fritz Grunewald, Heinrich Heine Universität, Düsseldorf, Germany
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Contemporary Mathematics
2000; 310 pp; softcover
Volume: 262
ISBN-10: 0-8218-2001-X
ISBN-13: 978-0-8218-2001-8
List Price: US$96 Member Price: US$76.80
Order Code: CONM/262

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.

Graduate students and research mathematicians interested in group theory and generalizations, topological groups, and Lie groups.

• Y. Benoist -- Tores affines
• C. Casacuberta -- On structures preserved by idempotent transformations of groups and homotopy types
• V. Charette and W. M. Goldman -- Affine Schottky groups and crooked tilings
• K. Dekimpe -- Polynomial structures on polycyclic groups: Recent developments
• B. Farb and L. Mosher -- Problems on the geometry of finitely generated solvable groups
• W. M. Goldman and G. A. Margulis -- Flat Lorentz 3-manifolds and cocompact Fuchsian groups
• O. Baues -- Varieties of discontinuous groups
• D. Burde -- Affine cohomology classes for filiform Lie algebras
• C. Cassidy, N. Kennedy, and D. Scevenels -- Hyperbolic automorphisms for groups in $$\mathcal{T}(4,2)$$
• S. Dupont -- Variétés projectives á holonomie dans le groupe $$\mathrm{Aff}^{+}({\mathbf R})$$
• Y. Kamishima -- Classification of homogeneous complex affinely flat surfaces with compact quotients and applications to complex projective structures
• Y. Kamishima and T. Udono -- On the fundamental groups of compact complete quaternionic affinely flat 2-manifolds
• W. Malfait -- An obstruction to the existence of Anosov diffeomorphisms on infra-nilmanifolds
• N. O'Sullivan -- Genus and localization of virtually nilpotent groups
• A. Parreau -- Immeubles affines: construction par les normes et étude des isométries
• J. A. Wolf -- Isoclinic spheres and flat homogeneous pseudo-Riemannian manifolds