23 papers
Bridge numbers of virtual graphs and handlebody-links
Nikolaos Chantis, Puttipong Pongtanapaisan
We study bridge indices of graphs, virtual graphs, and their handlebody classes. We construct virtual ravels for which the difference between bridge index and weighted overpass bri…
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…
Entanglement complexity of spanning pairs of lattice polygons
Ryan Blair, Puttipong Pongtanapaisan, Christine E. Soteros
We study the entanglement complexity of a system consisting of two simple-closed curves (self-avoiding polygons) that span a lattice tube, referred to as a 2SAP. 2SAPs are of inter…
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…
Estimating distances in simplicial complexes with applications to 3-manifolds and handlebody-knots
Sayantika Mondal, Puttipong Pongtanapaisan, Hanh Vo
We study distance relations in various simplicial complexes associated with low-dimensional manifolds. In particular, complexes satisfying certain topological conditions with verti…
Biquandles, quivers and virtual bridge indices
Tirasan Khandhawit, Puttipong Pongtanapaisan, Brandon Wang
We investigate connections between biquandle colorings, quiver enhancements, and several notions of the bridge numbers for virtual links, where . We show that for a…