32 citations · 64 across the 16 of their papers we have counts for
20 papers
The freeness Index of a graph
Abigail Thompson
We define a new integer invariant of a finite graph G, the freeness index, that measures the extent to which G can be embedded in the 3-sphere so that it and its subgraphs have ``s…
Cubic graphs induced by bridge trisections
Jeffrey Meier, Abigail Thompson, Alexander Zupan
Every embedded surface in the 4-sphere admits a bridge trisection, a decomposition of into three simple pieces. In this case, the surface $\mathca…
Trisections and link surgeries
Robion Kirby, Abigail Thompson
We examine questions about surgery on links which arise naturally from the trisection decomposition of 4-manifolds developed by Gay and Kirby. These links lie on Heegaard surfaces…
Tangle decompositions of alternating link complements
Joel Hass, Abigail Thompson, Anastasiia Tsvietkova
Decomposing knots and links into tangles is a useful technique for understanding their properties. The notion of prime tangles was introduced by Kirby and Lickorish in [3]; Lickori…
Alternating links have at most polynomially many Seifert surfaces of fixed genus
Joel Hass, Abigail Thompson, Anastasiia Tsvietkova
Let be a non-split prime alternating link with crossings. We show that for each fixed , the number of genus- Seifert surfaces for is bounded by an explicitly gi…
Dehn surgery on complicated fibered knots in the 3-sphere
Abigail Thompson
Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K is sufficiently complicated, then Dehn surgery on K cannot yield a lens space. Work of Yi Ni shows that…