Slice Knot
المؤلف:
Casson, J. and Gordon, C. M.
المصدر:
"Cobordism of Classical Knots." Preprint of Lecture. Orsay. 1975.
الجزء والصفحة:
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26-6-2021
1703
Slice Knot
A knot 
in 
is a slice knot if it bounds a disk 
in 
which has a tubular neighborhood 
whose intersection with 
is a tubular neighborhood 
for 
.
Every ribbon knot is a slice knot, and it is conjectured that every slice knot is a ribbon knot.
The knot determinant of a slice knot is a square number (Rolfsen 1976, p. 224).
Slice knots include the unknot (Rolfsen 1976, p. 226), square knot (Rolfsen 1976, p. 220), stevedore's knot 
, and 
(Rolfsen 1976, p. 225), illustrated above.
Casson and Gordon (1975) showed that the unknot and stevedore's knot are the only twist knots that are slice knots (Rolfsen 1976, p. 226).
REFERENCES:
Casson, J. and Gordon, C. M. "Cobordism of Classical Knots." Preprint of Lecture. Orsay. 1975.
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 218-220, 1976.
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