Читать книгу Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory - Vassily Olegovich Manturov - Страница 9

In the present chapter we discuss certain basic notions of combinatorial group theory. In particular, we recall the notion of small cancellation conditions for groups and study the diagrammatic method of describing such groups.

In a sense this approach (made possible by the van Kampen lemma (1933) giving a geometric interpretation of group relations) is the first example of the main principle this book is devoted to: how to study different objects (in our case — groups) with geometric, “picture-valued” instruments; how to construct a picture which contains all the important information about the studied object.