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

DOI:
https://doi.org/10.1090/S0002-9947-98-01651-1

MathSciNet review:
1357391

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Abstract | References | Similar Articles | Additional Information

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 elements which normally generates the free group of rank , 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 in . We shall also prove an analogous existence theorem for calibrations of -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:
https://doi.org/10.1090/S0002-9947-98-01651-1

Received by editor(s):
May 16, 1995

Received by editor(s) in revised form:
October 30, 1995

Article copyright:
© Copyright 1998
American Mathematical Society