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Plane graphs and link invariants

✍ Scribed by François Jaeger

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
803 KB
Volume
114
Category
Article
ISSN
0012-365X

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✦ Synopsis

A (tame) link can be defined as a finite collection of disjoint polygons embedded in Euclidean 3-space. Links are usually represented by plane projections, or diagrams, which can be viewed as 4-regular plane graphs with signed vertices. Then the 3-dimensional concept of ambient isotopy of links can be described in combinatorial terms on diagrams. This allows the definition of link invariants as valuations of diagrams which are invariant under certain simple local transformations. This approach has received much attention in recent years and has led to the solution of old problems in knot theory. Moreover, it brings a new dimension to the classical theory of plane graphs. We illustrate this by a survey of new results and problems with knot-theoretic meaning and purely combinatorial form.

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