algebraic link

{{Short description|Subclass of links in knot theory}}

File:Algebraic Borromean link diagram.svg 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.{{cite journal

| last = Thistlethwaite | first = Morwen B. | author-link = Morwen Thistlethwaite

| issue = 2

| journal = Pacific Journal of Mathematics

| mr = 1132393

| pages = 317–333

| title = On the algebraic part of an alternating link

| url = https://projecteuclid.org/euclid.pjm/1102637085

| volume = 151

| year = 1991}} Algebraic links are also called arborescent links.{{cite journal|last1=Gabai|first1=David|authorlink=David Gabai| title=Genera of the arborescent links|journal=Memoirs of the American Mathematical Society|date=1986|volume=59|issue=339|pages=1–98|doi=10.1090/memo/0339|url=https://www.ams.org/books/memo/0339/|url-access=subscription}}

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.{{cite encyclopedia|title=Encyclopaedia of Mathematics, Supplement III, Volume 13|first=Michiel|last=Hazewinkel|isbn=9781556080104|publisher=Springer|year=2001|page=34|url=https://books.google.com/books?id=47YC2h295JUC&pg=PA34}}.