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

 

Realizing homology boundary links
with arbitrary patterns


Author: Paul Bellis
Journal: Trans. Amer. Math. Soc. 350 (1998), 87-100
MSC (1991): Primary 57Q45, 57M07, 57M15
MathSciNet review: 1357391
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Abstract: Homology boundary links have become an increasingly important class of links, largely due to their significance in the ongoing concordance classification of links. Tim Cochran and Jerome Levine defined an algebraic object called a pattern associated to a homology boundary link which can be used to study the deviance of a homology boundary link from being a boundary link. Since a pattern is a set of $m$ elements which normally generates the free group of rank $m$, any invariants which detect non-trivial patterns can be applied to the purely algebraic question of when such a set is a set of conjugates of a generating set for the free group. We will give a constructive geometric proof that all patterns are realized by some homology boundary link $L^n$ in $S^{n+2}$. We shall also prove an analogous existence theorem for calibrations of $\mathbb{E}$-links, a more general and less understood class of links tha homology boundary links.


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Additional Information

Paul Bellis
Affiliation: Department of Mathematics, Rice University, P. O. Box 1892, Houston, Texas 77251-1892
Address at time of publication: 7932 Butterfield Dr., Elkridge, Maryland 21075
Email: apbellis@erols.com

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01651-1
PII: S 0002-9947(98)01651-1
Received by editor(s): May 16, 1995
Received by editor(s) in revised form: October 30, 1995
Article copyright: © Copyright 1998 American Mathematical Society