Classifying 1-handles attached to knotted surfaces

Boyle, Jeffrey

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

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ISSN 1088-6850(online) ISSN 0002-9947(print)

Classifying -handles attached to knotted surfaces

Author: Jeffrey Boyle
Journal: Trans. Amer. Math. Soc. 306 (1988), 475-487
MSC: Primary 57Q45; Secondary 57M99
MathSciNet review: 933302
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Abstract: We study a method of obtaining knotted surfaces in the -sphere ${S^4}$ by attaching embedded -dimensional -handles to a given knot. The main result is there is a one-to-one correspondence between the -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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