33 citations · 168 across the 48 of their papers we have counts for
54 papers
The stable Andrews-Curtis conjecture and thickenable presentations of the trivial group
Marc Lackenby
We establish an explicit upper bound on the number of stable Andrews-Curtis moves that convert thickenable balanced presentations of the trivial group to the standard one-generator…
Every finite group admits a just finite presentation
Marc Lackenby
A finite presentation < X | R > of a finite group is called `just finite' if removing any relation from R results in a presentation for an infinite group. It has been an open quest…
Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold
Marc Lackenby, Anastasiia Tsvietkova
We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant , properly embedded in a finite-vol…
A polynomial upper bound on Reidemeister moves for each link type
Marc Lackenby
For each link type in the 3-sphere, we show that there is a polynomial such that any two diagrams of with and crossings differ by at most $p_K(c_1) + p_K(…
How does over-squashing affect the power of GNNs?
Francesco Di Giovanni, T. Konstantin Rusch, Michael M. Bronstein +4
Graph Neural Networks (GNNs) are the state-of-the-art model for machine learning on graph-structured data. The most popular class of GNNs operate by exchanging information between…
The triangulation complexity of elliptic and sol 3-manifolds
Marc Lackenby, Jessica S. Purcell
The triangulation complexity of a compact 3-manifold is the minimal number of tetrahedra in any triangulation of the 3-manifold. We compute the triangulation complexity of all elli…