The Ranks of the Groups of Links

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The group of links in codimension greater than two is the group of isotopy classes of smooth embeddings , where are positive integers. A link is primary, if it becomes trivial after removing any of its components. This application computes the rank of the group of primary links of given dimensions .

Contributed by: Mikhail Skopenkov (May 2011)
(Institute for Information Transmission Problems of the Russian Academy of Sciences, and King Abdullah University of Science and Technology)
Open content licensed under CC BY-NC-SA



This application is based on the formula given in [1].


[1] D. Crowley, S. C. Ferry, and M. Skopenkov, "The Rational Classification of Links of Codimension > 2." (May 2011)

[2] A. Haefliger, "Differentiable Links," Topology, 1, 1962 pp. 241–244.

[3] V. Nezhinsky, "Some Computations in Higher Dimensional Link Theory," Siberian Mathematical Journal, 24(4), 1982 pp. 104–115 (in Russian).

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