arXiv subjects

Ella Pfaff

Publications and source records attributed to Ella Pfaff.

2 recordsLinked to original sources

arXiv2025

The Plain Sphere Number of a Link

Let $L$ be a link in $S^3$. We consider the class of meridional presentations for $\pi_1(S^3\backslash L)$ in which the relations are witnessed by embedded two-spheres which can be represented simultaneously in a fixed diagram of $L$, analogously to decomposition spheres studied by Cromwell, Menasco and others. Wirtinger relations are witnessed by such spheres and the Wirtinger presentation is a special case of the ones we study. We prove that the smallest number of generators of $\pi_1(S^3\backslash L)$ over all such presentations equals the bridge number of $L$.

math.GT↗

arXiv2024

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

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 bridge numbers in our construction fit into the equality $\beta(L\cup U)=2\beta(L)-1=\text{rank}(\pi_1(S^3\backslash (L\cup U)))$. In addition, we prove the MRC for new infinite families of links and distinguish them from previously settled cases through an application of bridge distance.

math.GT↗