Doubled Knot
المؤلف:
Livingston, C.
المصدر:
Knot Theory. Washington, DC: Math. Assoc. Amer.
الجزء والصفحة:
...
20-6-2021
1934
Doubled Knot
Let 
be the knot above, and let the homomorphism 
taking a knot 
to its companion knot 
be faithful (i.e., taking the preferred longitude and meridian of the original torus to the referred longitude and latitude of the tubular neighborhood). Then 
is an untwisted doubled knot of 
. Otherwise, 
is a doubled knot with 
twists (Rolfsen 1976, p. 112).
REFERENCES:
Livingston, C. Knot Theory. Washington, DC: Math. Assoc. Amer., pp. 35, 73, 146, and 154-155, 1993.
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 112, 166-167, and 225, 1976.
Whitehead, J. H. C. "On Doubled Knots." J. London Math. Soc. 12, 63-71, 1937.
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