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math.GT2026
Three thousand obstructions to knotless embedding
Thomas W Mattman, Andrei Pavelescu
We present a list of 3028 obstructions to knotless embedding. We survey recent work in this area including: 1) A bibliography of graphs proven to be intrinsically knotted without r…
math.GT2025
Boundary slopes (nearly) bound exceptional slopes
Kazuhiro Ichihara, Thomas W. Mattman
For a hyperbolic knot in , Dehn surgery along slope $r \in \Q \cup \{\frac10\}$ is {\em exceptional} if it results in a non-hyperbolic manifold. We say meridional surgery, $r…
math.GT2024
Dips at small sizes for topological graph obstruction sets
Hyoungjun Kim, Thomas W. Mattman
The Graph Minor Theorem of Robertson and Seymour implies a finite set of obstructions for any minor closed graph property. We show that there are only three obstructions to knotles…