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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

HNN bases and high-dimensional knots


Author: Daniel S. Silver
Journal: Proc. Amer. Math. Soc. 124 (1996), 1247-1252
MSC (1991): Primary 57Q45; Secondary 20E06, 20F05
MathSciNet review: 1343725
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Abstract: There exists a $3$-knot group having HNN bases of two types: bases that are arbitrarily large finitely presented and bases that are arbitrarily large finitely generated but not finitely presented. Any $n$-knot with such a group has a Seifert manifold that can be converted to a minimal one by a finite sequence of ambient - and $1$-surgeries, but cannot be converted by $1$-surgeries alone.


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Additional Information

Daniel S. Silver
Affiliation: Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688
Email: silver@mathstat.usouthal.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03520-4
PII: S 0002-9939(96)03520-4
Received by editor(s): May 17, 1994
Communicated by: James West
Article copyright: © Copyright 1996 American Mathematical Society