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.