Contemporary Mathematics 2000; 310 pp; softcover Volume: 262 ISBN10: 082182001X ISBN13: 9780821820018 List Price: US$91 Member Price: US$72.80 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 3manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infranilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered highlevel 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. Readership Graduate students and research mathematicians interested in group theory and generalizations, topological groups, and Lie groups. Table of Contents  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 3manifolds 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 2manifolds
 W. Malfait  An obstruction to the existence of Anosov diffeomorphisms on infranilmanifolds
 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 pseudoRiemannian manifolds
