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Bridge Multisections of Knotted Surfaces in \\(S^4\\)
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Paper
Bridge Multisections of Knotted Surfaces in \\(S^4\\)
2026
Overview
Bridge multisections are combinatorial descriptions of surface links in 4-space using tuples of trivial tangles. They were introduced by Islambouli, Karimi, Lambert-Cole, and Meier to study curves in rational surfaces. In this paper, we prove a uniqueness result for bridge multisections of surfaces in 4-space: we give a complete set of moves relating to any two multiplane diagrams of the same surface. This is done by developing a surgery operation on multiplane diagrams called band surgery. Another application of this surgery move is that any \\(n\\)-valent graph with an \\(n\\)-edge coloring is the spine of a bridge multisection for an unknotted surface. We also prove that any multisected surface in \\(S^4\\) can be unknotted by finitely many band surgeries.
Publisher
Cornell University Library, arXiv.org
Subject
