TL;DR
This paper introduces the concept of alteration of surfaces in 3-manifolds, extending the idea of compression, and shows that any two Seifert surfaces of the same link are related by a single alteration.
Contribution
The paper extends the notion of compression to a broader class of surface modifications called alterations, providing a new way to relate Seifert surfaces.
Findings
Any two Seifert surfaces of the same link are related by a single alteration.
Alteration generalizes compression for surfaces in 3-manifolds.
Abstract
We introduce the notion of alteration of a surface embedded in a 3-manifold extending that of compression. We see that given two Seifert surfaces of the same link are related to each other by ``single'' alteration, even if they are not by compression.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals