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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classifying $ 1$-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 $ 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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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0933302-X
PII: S 0002-9947(1988)0933302-X
Article copyright: © Copyright 1988 American Mathematical Society