  The "peak reduction" method is a powerful combinatorial technique with
applications in many different areas of mathematics as well as theoretical
computer science. It was introduced by Whitehead, a famous topologist and group
theorist, who used it to solve an important algorithmic problem concerning
automorphisms of a free group. Since then, this method was used to solve
numerous problems in group theory, topology, combinatorics, and probably in
some other areas as well.
  In this paper, we give a survey of what seems to be the first applications of
the peak reduction technique in commutative algebra and affine algebraic
geometry.
