Algebraic link

In the mathematical field of knot theory, an algebraic link is a link that can be decomposed by Conway spheres into 2-tangles.[1] Algebraic links are also called arborescent links.[2] Although algebraic links and algebraic tangles were originally defined by John H. Conway as having two pairs of open ends, they were subsequently generalized to more pairs.[3]

Decomposition of the Borromean rings by a Conway sphere (black dotted vertical midline) into two 2-tangles, showing that the Borromean rings form an algebraic link

References

Thistlethwaite, Morwen B. (1991). "On the algebraic part of an alternating link". Pacific Journal of Mathematics. 151 (2): 317–333. MR 1132393.
Gabai, David (1986). "Genera of the arborescent links". Memoirs of the American Mathematical Society. 59 (339): 1–98. doi:10.1090/memo/0339.
Hazewinkel, Michiel (2001). Encyclopaedia of Mathematics, Supplement III, Volume 13. Springer. p. 34. ISBN 9781556080104..

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[1] Thistlethwaite, Morwen B. (1991). "On the algebraic part of an alternating link". Pacific Journal of Mathematics. 151 (2): 317–333. MR 1132393.

[2] Gabai, David (1986). "Genera of the arborescent links". Memoirs of the American Mathematical Society. 59 (339): 1–98. doi:10.1090/memo/0339.

[3] Hazewinkel, Michiel (2001). Encyclopaedia of Mathematics, Supplement III, Volume 13. Springer. p. 34. ISBN 9781556080104..