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Book Cover
Author Igodt, Paul

Title Crystallographic Groups and Their Generalizations
Published Providence : American Mathematical Society, 2000


Description 1 online resource (330 pages)
Series Contemporary Mathematics ; v. 262
Contemporary Mathematics
Contents ""Contents""; ""Preface""; ""List of participants""; ""Titles of talks and posters""; ""Tores affines""; ""On structures preserved by idempotent transformations of groups and homotopy types""; ""Affine Schottky groups and crooked tilings""; ""1. Minkowski space""; ""1.1. Minkowski space and its projectivization""; ""1.2. A little Euclidean geometry""; ""1.3. Null frames""; ""2. Schottky groups""; ""2.1. Schottky's configuration""; ""2.2. Existence of a small interval""; ""2.3. A criterion for Ñ?-hyperbolicity""; ""3. Crooked planes and zigzags""
""3.1. Extending Schottky groups to Minkowski space""""3.2. Construction of a crooked plane""; ""3.3. Zigzags""; ""3.4. Affine deformations""; ""4. Completeness""; ""4.1. Construction of the nested sequence""; ""4.2. Uniform Euclidean width of crooked polyhedra""; ""4.3. Approximating zigzag regions by half-planes""; ""4.4. Bounding the separation of half-planes""; ""4.6. Changing the hyperbolicity""; ""Polynomial structures on polycyclic groups: Recent developments""; ""Problems on the geometry of finitely generated solvable groups""; ""1. Introduction""; ""2. Dioubina's examples""
""3. Nilpotent groups and Pansu's Theorem""""4. Abelian-by-cyclic groups: nonpolycyclic case""; ""5. Abelian-by-cyclic groups: polycyclic case""; ""References""; ""Flat Lorentz 3-manifolds and cocompact Fuchsian groups""; ""Varieties of discontinuous groups""; ""Affine cohomology classes for filiform Lie algebras""; ""Hyperbolic automorphisms for groups in 7(4, 2)""; ""Variétés projectives à holonomie dans le groupe Aff+ (R)""; ""Classification of homogeneous complex affinely flat surfaces with compact quotients and applications to complex projective structures""
""On the fundamental groups of compact complete quaternionic affinely flat 2-manifolds""""An obstruction to the existence of Anosov diffeomorphisms on infra-nilmanifolds""; ""Genus and localization of virtually nilpotent groups""; ""Immeubles affines: construction par les normes et étude des isométries""; ""Introduction""; ""1. D�finitions et caractérisations des immeubles affines.""; ""1.1. La structure mod�le.""; ""1.2. Définition des immeubles affines.""; ""1.3. Premi�res définitions.""; ""1.4. Deux conséquences de l'axiome (A5').""
""1.6. L'immeuble des germes en un point et la propriété (A3').""""1.7. Rétractions.""; ""1.8. Vérification de l'axiome (A4).""; ""2. Décomposition et propriétés géométriques des immeubles affines.""; ""2.1. Produits et décomposition""; ""2.2. Automorphismes et isométries.""; ""2.3. Géométrie CAT(O).""; ""2.4. Enveloppe convexe de Weyl de deux points.""; ""2.5. Isométries préservant le type des segments.""; ""2.6. Le syst�me maximal d'appartements.""; ""2.7. La définition de Kleiner-Leeb.""; ""3. Construction de l'immeuble de GLn(F).""; ""3.1. Normes ultramétriques.""
Notes ""3.2. Définition de l'immeuble de GL(V).""
Print version record
Subject Crystallography, Mathematical -- Congresses
Group theory -- Congresses
Crystallography, Mathematical.
Group theory.
Genre/Form Conference papers and proceedings.
Form Electronic book
Author Abels, Herbert
Félix, Yves
ISBN 9780821878521