Isotopy invariants of graphs

Jonish, D.; Millett, K. C.

doi:10.1090/S0002-9947-1991-1062189-2

Isotopy invariants of graphs
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by D. Jonish and K. C. Millett

Trans. Amer. Math. Soc. 327 (1991), 655-702

DOI: https://doi.org/10.1090/S0002-9947-1991-1062189-2

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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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