5 papers
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…
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.…
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…
Studying links via booklinks: A Markov theorem
Roman Aranda, Fraser Binns, Margaret Doig
We introduce "book links" as a generalization of braids in open book decompositions; this new class of objects includes both braids and plats as special cases. We then prove a vers…
Minimal genus four manifolds
Román Aranda
In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the Euler characteristic of and the rank of its fundamental group…