Browsing by Author "Bellis, Paul Andrew"
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Item Homology boundary links, patterns, and Seifert forms(1996) Bellis, Paul Andrew; Cochran, Tim D.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 an homology boundary link, which can be used to study the deviance of an 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. This thesis contains two major results. First, we will give a constructive geometric proof that all patterns are realized by some ribbon homology boundary link $\rm L\sp{n}$ in $\rm S\sp{n+2}$ We shall also prove an analogous existence theorem for calibrations of ${\rm I\!E}$-links, a more general and less understood class of links than homology boundary links. Second, we will prove that given a boundary link L and Seifert system V for L admitting pattern $\rm P\sb{L}$, the strong fusion of L along multiple fusion bands, denoted SF(L), is an homology boundary link possessing particular generalized Seifert system Y admitting specific pattern $\rm P\sb{SF(L)}$.