Geometry of Crystallographic Groups

"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;"--