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Isotopy invariants of graphs


Authors: D. Jonish and K. C. Millett
Journal: Trans. Amer. Math. Soc. 327 (1991), 655-702
MSC: Primary 57M25; Secondary 05C10
DOI: https://doi.org/10.1090/S0002-9947-1991-1062189-2
MathSciNet review: 1062189
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Abstract: The development of oriented and semioriented algebraic invariants associated to a class of embeddings of regular four valent graphs is given. These generalize the analogous invariants for classical knots and links, can be determined from them by means of a weighted averaging process, and define them by means of a new state model. This development includes the elucidation of the elementary spatial equivalences (generalizations of the classical Reidemeister moves), and the extension of fundamental concepts in classical knot theory, such as the linking number, to this class spatial graphs.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1062189-2
Keywords: Spatial graphs, knot theory, oriented and semioriented polynomial invariants
Article copyright: © Copyright 1991 American Mathematical Society

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