By J Scott Carter
the purpose of this ebook is to provide as specified an outline as is feasible of 1 of the main attractive and complex examples in low-dimensional topology. this instance is a gateway to a brand new notion of upper dimensional algebra during which diagrams change algebraic expressions and relationships among diagrams symbolize algebraic family members. The reader may possibly study the adjustments within the illustrations in a leisurely type; or with scrutiny, the reader becomes regular and strengthen a facility for those diagrammatic computations.
The textual content describes the basic topological rules 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 proficient reader will enjoy the casual advent of rules. This quantity also will attract scientifically literate people who enjoy mathematical beauty.
- A Sphere
- Surfaces, Folds, and Cusps
- The within and Outside
- Immersed Surfaces
- 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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