AN OBSTRUCTION TO EMBEDDING 4-TANGLES IN LINKS
1999 ◽
Vol 08
(03)
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pp. 321-352
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Keyword(s):
We consider the ways in which a 4-tangle T inside a unit cube can be extended outside the cube into a knot or link L. We present two links n(T) and d(T) such that the greatest common divisor of the determinants of these two links always divides the determinant of the link L. In order to prove this result we give a two-integer invariant of 4-tangles. Calculations are facilitated by viewing the determinant as the Kauffman bracket at a fourth root of -1, which sets the loop factor to zero. For rational tangles, our invariant coincides with the value of the associated continued fraction.
2019 ◽
Vol 28
(14)
◽
pp. 1950083
◽
Keyword(s):
1998 ◽
Vol 07
(05)
◽
pp. 659-700
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2020 ◽
Vol 25
(2)
◽
pp. 125-132
2017 ◽
Vol 26
(12)
◽
pp. 1750081
Keyword(s):