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.


  • 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.

Show description

Read or Download An Excursion in Diagrammatic Algebra:Turning a Sphere from Red to Blue: 48 (Series on Knots and Everything) PDF

Similar geometry & topology books

Canterbury Cathedral

Trust within the Heavenly nature of geometrical kinds has existed seeing that prehistoric instances, yet basically now, in those pages, will we see and know how this trust encouraged the layout of an excellent spiritual development. with out mathematical complexities, yet in uncomplicated language and with many clarifying illustrations, the writer demonstrates the geometrical structures that the nice architects of Canterbury Cathedral devised to carry the geometry in their development into concord with that of the Universe, and with the geometries in their predecessors.

The Heart of Cohomology

In case you have now not heard approximately cohomology, the guts of Cohomology can be suited to you. The e-book supplies primary notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived different types are defined in trouble-free type. purposes to sheaf cohomology.

Introductory Topology:Exercises and Solutions

The e-book bargains a very good creation to topology via solved workouts. it truly is regularly meant for undergraduate scholars. such a lot workouts are given with distinctive suggestions. Contents:Exercises and Solutions:General Notions: units, services et al. Metric SpacesTopological SpacesContinuity and ConvergenceCompact SpacesConnected SpacesComplete Metric SpacesFunction SpacesReadership: Undergraduate scholars and academics in topology.

Introduction to Set Theory and Topology (International Series in Pure and Applied Mathematics)

Creation to Set idea and Topology describes the elemental innovations of set idea and topology in addition to its applicability to research, geometry, and different branches of arithmetic, together with algebra and likelihood concept. thoughts reminiscent of inverse restrict, lattice, excellent, clear out, commutative diagram, quotient-spaces, thoroughly general areas, quasicomponents, and cartesian items of topological areas are thought of.

Additional info for An Excursion in Diagrammatic Algebra:Turning a Sphere from Red to Blue: 48 (Series on Knots and Everything)

Sample text

Download PDF sample

Rated 4.40 of 5 – based on 48 votes