A01=Andrzej Szczepanski
Author_Andrzej Szczepanski
Category=PBWH
Category=PNT
Crystallographic Groups
Discontinuous Groups of Transformation
Discrete Subgroups of Lie Groups
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Euclidean Geometry
Flat Manifolds
Homogeneous Manifolds
Infinite Groups
Product details
- ISBN 9789814412254
- Publication Date: 11 Oct 2012
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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Crystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. They got their name, because in three dimensions they occur as the symmetry groups of a crystal (which we imagine to extend to infinity in all directions). The book is divided into two parts. In the first part, the basic theory of crystallographic groups is developed from the very beginning, while in the second part, more advanced and more recent topics are discussed. So the first part of the book should be usable as a textbook, while the second part is more interesting to researchers in the field. There are short introductions to the theme before every chapter. At the end of this book is a list of conjectures and open problems. Moreover there are three appendices. The last one gives an example of the torsion free crystallographic group with a trivial center and a trivial outer automorphism group.This volume omits topics about generalization of crystallographic groups to nilpotent or solvable world and classical crystallography. We want to emphasize that most theorems and facts presented in the second part are from the last two decades. This is after the book of L Charlap “Bieberbach groups and flat manifolds” was published.
