Abstract
Any two knots admit orientation preserving homeomorphic Seifert surfaces, as can be seen by stabilizing. There is a generalization of a Seifert surface to the setting of links called a [Formula: see text]-complex. In this paper, we ask when two links will admit orientation preserving homeomorphic [Formula: see text]-complexes. In the case of 2-component links, we find that the pairwise linking number provides a complete obstruction. In the case of links with 3 or more components and zero pairwise linking number, Milnor’s triple linking number provides a complete obstruction.
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