Algebraic link

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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 Algebraic Borromean link diagram.svg
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

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]

References

  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..
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