Small Knots and Large Handle Additions

Keywords

handlebody / simple small knot / orientable manifold / 57N10

References

[1] Thurston W. Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Am. Math. Soc., 1982, 6: 357-388.

[2] Gordon C. Dehn Filling: A Survey, Knot Theory, 1998, Warsaw, Poland: Banach Center Publications.

[3] Hatcher A. On the boundary curves of incompressible surfaces. Pac. J. Math., 1982, 99: 373-377.

[4] Scharlemann M., Wu Y. Hyperbolic manifolds and degenerating handle additions. J. Aust. Math. Soc., Ser. A, 1993, 55: 72-89.

[5] Lackenby M. Attaching handlebody to 3-manifolds. Geom. Topol., 2002, 6: 889-904.

[6] Qiu R. F. Incompressible surfaces in handlebodies and closed 3-manifolds of Heegaard genus two. Proc. Am. Math. Soc., 2000, 128: 3091-3097.

[7] Jaco W. Adding a 2-handle to a 3-manifold, an application to property R. Proc. Am. Math. Soc., 1984, 92: 288-292.

[8] Culler M., Gordon C., Luecke J., Shalen P. Cyclic surgery on knots. Ann. Math., 1987, 125: 237-300.