Classifying 1-handles attached to knotted surfaces

Boyle, Jeffrey

doi:10.1090/S0002-9947-1988-0933302-X

Classifying $1$-handles attached to knotted surfaces
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Trans. Amer. Math. Soc. 306 (1988), 475-487 Request permission

Abstract:

We study a method of obtaining knotted surfaces in the $4$-sphere ${S^4}$ by attaching embedded $2$-dimensional $1$-handles to a given knot. The main result is there is a one-to-one correspondence between the $1$-handles that can be attached to a knot and the double cosets of the peripheral subgroup in the group of the knot. Many examples and applications are given.

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