Geometry of Crystallographic Groups PDF
By:Andrzej Szczepański
Published on 2012-08-30 by World Scientific
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. Contents:DefinitionsBieberbach TheoremsClassification MethodsFlat Manifolds with b1 = 0Outer Automorphism GroupsSpin Structures and Dirac OperatorFlat Manifolds with Complex StructuresCrystallographic Groups as Isometries of ℍnHantzsche–Wendt GroupsOpen Problems Readership: Researchers in geometry and topology, algebra and number theory and chemist. Keywords:Crystallographic Groups;Flat Manifolds;Euclidean Geometry;Discontinuous Groups of Transformation;Discrete Subgroups of Lie Groups;Homogeneous Manifolds;Infinite GroupsKey Features:New materials from the last two decades, the crystallographic groups are presented from the very beginning with details proofs of the classical Bieberbach theoremsReviews: |This very precise and well written text is an extended version of the notes of the lectures given by the author at Gdańsk University for graduate students in the academic year 2004/05.| The European Mathematical Society
This Book was ranked at 18 by Google Books for keyword Crystallography.
Book ID of Geometry of Crystallographic Groups's Books is 4-u6CgAAQBAJ, Book which was written byAndrzej Szczepańskihave ETAG "9I4alS8Ze9Q"
Book which was published by World Scientific since 2012-08-30 have ISBNs, ISBN 13 Code is 9789814412278 and ISBN 10 Code is 9814412279
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