This highly readable text details the interaction between the mathematical theory of knots and the theories of surfaces and group presentations. It expertly introduces several topics critical to the development of pure mathematics while providing an account of math "in action" in an unusual context. Beginning with a simple diagrammatic approach to the study of knots that reflects the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent research advances. Topics include topological spaces, surfaces, the fundamental group, graphs, free groups,...

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.
A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes...