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math.GT2025
Trisected Rainbows and Braids
Román Aranda, Scott Carter, Julia Courtney +1
New explicit procedures for passing among triplane diagrams, braid movies, and braid charts for knotted surfaces in are presented. To this end, rainbow diagrams, whi…
math.GT2025
Region colorings of surfaces in 4-space
Román Aranda, Noah Crawford, Andrew Maas +6
Niebrzydowski introduced a theory of region colorings for surface links. In this paper, we translate the coloring invariant to the context of triplane diagrams and movies of knots.…
math.GT2025
Manifolds with weakly reducible genus-three trisections are standard
Román Aranda, Alexander Zupan
Heegaard splittings stratify 3-manifolds by complexity; only admits a genus-zero splitting, and only , , and lens spaces admit genus-one splitti…