Geometry of Crystallographic Groups (Second Edition) (English, Andrzej Szczepanski)

"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: New Presentation of Bieberbach Theorems; Methods of Classification; Flat Manifolds with the First Betti Number Zero; Symmetris of Flat Manifolds; Spin Structures and Dirac Operator; Flat Manifolds with Complex Structures; Crystallographic Groups as Isometries of Hyperbolic Space; Fenomen of Hantzsche-Wendt Groups; Open Problems;"--