A note concerning the 3-manifolds which span certain surfaces in the 4-ball

Trace, Bruce

doi:10.1090/S0002-9939-1988-0915740-X

A note concerning the $3$-manifolds which span certain surfaces in the $4$-ball
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Proc. Amer. Math. Soc. 102 (1988), 177-182 Request permission

Abstract:

We consider surfaces of the form $F{ \cup _K}D$ where $F$ is a Seifert surface and $D$ is a slicing disk for the knot $K$. We show that, in general, there is no $3$-manifold $M$ which spans $F{ \cup _K}D$ in the $4$-ball such that $F$ can be compressed to a disk in $M$.

References

John Stallings, On the loop theorem, Ann. of Math. (2) 72 (1960), 12–19. MR 121796, DOI 10.2307/1970146
Bruce Trace, Some comments concerning the Levine approach to slicing classical knots, Topology Appl. 23 (1986), no. 3, 217–235. MR 858332, DOI 10.1016/0166-8641(85)90041-0
Friedhelm Waldhausen, On irreducible $3$-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56–88. MR 224099, DOI 10.2307/1970594
E. C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965), 471–495. MR 195085, DOI 10.1090/S0002-9947-1965-0195085-8