Geometry of Crystallographic Groups

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Geometry of Crystallographic Groups by Andrzej Szczepański, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Andrzej Szczepański ISBN: 9789814412278
Publisher: World Scientific Publishing Company Publication: August 30, 2012
Imprint: WSPC Language: English
Author: Andrzej Szczepański
ISBN: 9789814412278
Publisher: World Scientific Publishing Company
Publication: August 30, 2012
Imprint: WSPC
Language: English

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:

  • Definitions
  • Bieberbach Theorems
  • Classification Methods
  • Flat Manifolds with b1 = 0
  • Outer Automorphism Groups
  • Spin Structures and Dirac Operator
  • Flat Manifolds with Complex Structures
  • Crystallographic Groups as Isometries of ℍn
  • Hantzsche–Wendt Groups
  • Open Problems

Readership: Researchers in geometry and topology, algebra and number theory and chemist.
Key Features:

  • New materials from the last two decades, the crystallographic groups are presented from the very beginning with details proofs of the classical Bieberbach theorems
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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:

Readership: Researchers in geometry and topology, algebra and number theory and chemist.
Key Features:

More books from World Scientific Publishing Company

Cover of the book Applied Trade Policy Modeling in 16 Countries by Andrzej Szczepański
Cover of the book Asian Free Trade Agreements and WTO Compatibility by Andrzej Szczepański
Cover of the book Optical Properties of Graphene by Andrzej Szczepański
Cover of the book From Micro to Macro by Andrzej Szczepański
Cover of the book Principles of Artificial Neural Networks by Andrzej Szczepański
Cover of the book Impossible Minds by Andrzej Szczepański
Cover of the book Insights on Singapore's Economy and Society from Leading Thinkers by Andrzej Szczepański
Cover of the book Ethical and Legal Issues in Modern Surgery by Andrzej Szczepański
Cover of the book Revealed Biodiversity by Andrzej Szczepański
Cover of the book China-EU by Andrzej Szczepański
Cover of the book The Cyprus Bail-in by Andrzej Szczepański
Cover of the book 2017 Annual Competitiveness Analysis and Impact of Exchange Rates on Foreign Direct Investment Inflows to Sub-National Economies of Indonesia by Andrzej Szczepański
Cover of the book Lectures on Quantum Computing, Thermodynamics and Statistical Physics by Andrzej Szczepański
Cover of the book Henri Poincaré by Andrzej Szczepański
Cover of the book Governing Society in Contemporary China by Andrzej Szczepański
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy