Excursion In Diagrammatic Algebra, An: Turning A Sphere From Red To Blue: Turning a Sphere from Red to Blue

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.

The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.

• A Sphere
• Surfaces, Folds, and Cusps
• The Inside and Outside
• Dimensions
• Immersed Surfaces
• Movies
• Movie Moves
• Taxonomic Summary
• How Not to Turn the Sphere Inside-Out
• A Physical Metaphor
• Sarah's Thesis
• The Eversion
• The Double Point and Fold Surfaces