Diagram geometry lies in the interaction between group theory and geometry and is an active area of research as it provides interesting combinatorial structures in geometry and shows how these can be applied to the classification of complex groups. This book provides a survey of research.
Diagram geometry provides a range of techniques that enable an interaction between group theory and geometry. These techniques allow the mathematician to get information on a multi-dimensional geometric object from some knowledge of its bi-dimensional properties. This book introduces these techniques and provides a survey of the development of the subject of diagram geometry.The first three chapters are descriptive; a number of examples are presented, basic concepts are explained, and the reader is introduced to the language of diagram geometries.The theory is developed in the next three chapters and in chapter 7 a number of characterizations are proved. This is continued in later chapters following a survey of more advanced concepts and techniques.
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