By J Scott Carter

the purpose of this publication is to offer as targeted an outline as is feasible of 1 of the main attractive and intricate examples in low-dimensional topology. this instance is a gateway to a brand new inspiration of upper dimensional algebra during which diagrams exchange algebraic expressions and relationships among diagrams symbolize algebraic kin. The reader may possibly research the adjustments within the illustrations in a leisurely style; or with scrutiny, the reader becomes prevalent and strengthen a facility for those diagrammatic computations.

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

Contents:

  • A Sphere
  • Surfaces, Folds, and Cusps
  • The inside of 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 element and Fold Surfaces

Readership: Researchers in mathematics.

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An Excursion in Diagrammatic Algebra:Turning a Sphere from Red to Blue: 48 (Series on Knots and Everything) by J Scott Carter


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