2024/10/02 by Aranda, Román, Engelhardt, Carolyn · 1 citation
#57Q45 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2410.01921
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 S4 can be unknotted by finitely many band surgeries.