An Excursion in Diagrammatic Algebra:Turning a Sphere from by J Scott Carter

By J Scott Carter

the purpose of this booklet is to offer as exact an outline as is feasible of 1 of the main appealing and intricate examples in low-dimensional topology. this instance is a gateway to a brand new concept of upper dimensional algebra within which diagrams exchange algebraic expressions and relationships among diagrams symbolize algebraic kinfolk. The reader could study the adjustments within the illustrations in a leisurely type; or with scrutiny, the reader becomes frequent and improve a facility for those diagrammatic computations.

The textual content describes the basic topological principles via metaphors which are skilled in way of life: shadows, the human shape, the intersections among partitions, and the creases in a blouse or a couple of trousers. Mathematically expert reader will enjoy the casual creation of rules. This quantity also will entice scientifically literate people who savor mathematical beauty.

Contents:

  • A Sphere
  • Surfaces, Folds, and Cusps
  • The within and Outside
  • Dimensions
  • Immersed Surfaces
  • Movies
  • Movie Moves
  • Taxonomic Summary
  • How to not flip the field Inside-Out
  • A actual Metaphor
  • Sarah's Thesis
  • The Eversion
  • The Double aspect and Fold Surfaces

Readership: Researchers in mathematics.

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