Adding a 2-handle to a 3-manifold: an application to property 𝑅

Jaco, William

doi:10.1090/S0002-9939-1984-0754723-6

Adding a $2$-handle to a $3$-manifold: an application to property $R$
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by William Jaco PDF

Proc. Amer. Math. Soc. 92 (1984), 288-292 Request permission

Abstract:

A sufficient condition is given for adding a $2$-handle to a $3$-manifold and obtaining a $3$-manifold with incompressible boundary. The main result is then used to show that a knot in the $3$-sphere admitting a partially unknotted spanning surface has Property $R$.

References

Robion Kirby and Paul Melvin, Slice knots and property $\textrm {R}$, Invent. Math. 45 (1978), no. 1, 57–59. MR 467754, DOI 10.1007/BF01406223
Howard Lambert, Longitude surgery on genus $1$ knots, Proc. Amer. Math. Soc. 63 (1977), no. 2, 359–362. MR 438322, DOI 10.1090/S0002-9939-1977-0438322-8
Louise E. Moser, On the impossibility of obtaining $S^{2}\times S^{1}$ by elementary surgery along a knot, Pacific J. Math. 53 (1974), 519–523. MR 358756, DOI 10.2140/pjm.1974.53.519

Incompressible surfaces in

-manifolds