1 citations · 1 across the 13 of their papers we have counts for
14 papers
Decompositions and diagrams of symplectic surfaces in Weinstein domains
Román Aranda, Patricia Cahn, Agniva Roy +1
We introduce combinatorial and diagrammatic methods for representing properly embedded symplectic surfaces in 4-dimensional Weinstein domains. We show that positive ascending surfa…
Bridge position of 3-manifolds embedded in the 5-sphere
Román Aranda, Sarah Blackwell, Geunyoung Kim +2
We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and t…
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…
Bridge Multisections of Knotted Surfaces in
Román Aranda, Carolyn Engelhardt
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…
Pants distances of knotted surfaces in 4-manifolds
Román Aranda, Sarah Blackwell, Devashi Gulati +4
We define a pants distance for knotted surfaces in 4-manifolds, which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine t…
A bound on the number of twice-punctured tori in a knot exterior
Román Aranda, Enrique Ramírez-Losada, Jesús Rodríguez-Viorato
This paper continues a program due to Motegi regarding universal bounds for the number of non-isotopic essential -punctured tori in the complement of a hyperbolic knot in .…
Bounds for Kirby-Thompson invariants of knotted surfaces
Román Aranda, Puttipong Pongtanapaisan, Cindy Zhang
We provide sharp lower bounds for two versions of the Kirby-Thompson invariants for knotted surfaces, one of which was originally defined by Blair, Campisi, Taylor, and Tomova. The…
Bounding the Kirby-Thompson invariant of spun knots
Román Aranda, Puttipong Pongtanapaisan, Scott A. Taylor +1
A bridge trisection of a smooth surface in is a decomposition analogous to a bridge splitting of a link in . The Kirby-Thompson invariant of a bridge trisection measures…
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…
Thin Position through the lens of trisections of 4-manifolds
Román Aranda
Motivated by M. Scharlemann and A. Thompson's definition of thin position of 3-manifolds, we define the width of a handle decomposition a 4-manifold and introduce the notion of thi…
Representativity and waist of cable knots
Román Aranda, Seungwon Kim, Maggy Tomova
We study the incompressible surfaces in the exterior of a cable knot and use this to compute the representativity and waist of most cable knots.