The Structure and Enumeration of Link Projections

Bridgeman, Martin

doi:10.1090/S0002-9947-96-01484-5

The Structure and Enumeration of Link Projections
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by Martin Bridgeman

Trans. Amer. Math. Soc. 348 (1996), 2235-2248

DOI: https://doi.org/10.1090/S0002-9947-96-01484-5

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Abstract:

We define a decomposition of link projections whose pieces we call atoroidal graphs. We describe a surgery operation on these graphs and show that all atoroidal graphs can be generated by performing surgery repeatedly on a family of well-known link projections. This gives a method of enumerating atoroidal graphs and hence link projections by recomposing the pieces of the decomposition.

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