It is eleven years since the First Edition of Geometry of Crystallographic Groups appeared. This Second Edition expands on the first, providing details of a new result of automorphism of crystallographic groups, and on Hantzsche-Wendt groups/manifolds.
Crystalographic groups are groups which act via isometries on some n-dimensional Euclidean space, so-named because in three dimensions they occur as the symmetry groups of a crystal. There are short introductions to the theme before every chapter, and a list of conjectures and open projects at the end of the book.
Geometry of Crystallographic Groups is suitable as a textbook for students, containing basic theory of crystallographic groups. It is also suitable for researchers in the field, discussing in its second half more advanced and recent topics.
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
- Combinatorial Hantzsche-Wendt Groups
- Open Problems
Readership: Researchers in geometry and topology, algebra and theory students, Institutes of Crystallography, University Chemistry departments.
Review of the First Edition: ‘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.’ – The European Mathematical Society
Key Features:
- This is a mathematical book, but crystallography is also a popular topic within Chemistry and Physics. It is therefore a useful book for students of all three of these
- This book builds on the work of L S Charlap, Bieberbach Groups and Flat Manifolds, with many fresh and important insights and results
- New materials from the last two decades are detailed clearly
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