Ryan Blair

activity

20242026

collaborators

4 papers

math.GT2026

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…

math.GT2025

Rep-Tiles

Ryan Blair, Patricia Cahn, Alexandra Kjuchukova +1

An $n$ -dimensional rep-tile is a compact, connected submanifold of $R^{n}$ with non-empty interior which can be decomposed into pairwise isometric rescaled copies of itself…

math.GT2025

The Plain Sphere Number of a Link

Ryan Blair, Alexandra Kjuchukova, Ella Pfaff

Let $L$ be a link in $S^{3}$ . We consider the class of meridional presentations for $I ¨ _{1} (S^{3} \ L)$ in which the relations are witnessed by embedded two-spheres which can be…

math.GT2024

Adding a suitable unknot to any link equates bridge number and meridional rank

Ryan Blair, Alexandra Kjuchukova, Ella Pfaff

Given any link $L \subseteq S^{3}$ , we show that it is possible to embed an unknot $U$ in its complement so that the link $L \cup U$ satisfies the Meridional Rank Conjecture (MRC). The…