The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.

Includes supplementary material: sn.pub/extras

Inhalt
I Groups.- 1 Classical Techniques of Combinatorial Group Theory.- 2 Test Elements.- 3 Other Special Elements.- 4 Automorphic Orbits.- II Polynomial Algebras.- 5 The Jacobian Conjecture.- 6 The Cancellation Conjecture.- 7 Nagata's Problem.- 8 The Embedding Problem.- 9 Coordinate Polynomials.- 10 Test Polynomials.- III Free Nielsen-Schreier Algebras.- 11 Schreier Varieties of Algebras.- 12 Rank Theorems and Primitive Elements.- 13 Generalized Primitive Elements.- 14 Free Leibniz Algebras.- References.- Notation Index.- Author Index.