6 papers
Incompressible surfaces, hierarchies and unknot recognition
Marc Lackenby
We present a new algorithm to determine whether a compact orientable surface properly embedded in a compact orientable 3-manifold is incompressible. As a special case, this provide…
Some fast algorithms for curves in surfaces
Marc Lackenby
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two proper…
Bounds for the number of moves between pants decompositions, and between triangulations
Marc Lackenby, Mehdi Yazdi
Given two pants decompositions of a compact orientable surface , we give an upper bound for their distance in the pants graph that depends logarithmically on their intersection…
On graphs, homology bases, and triangulated homology spheres
Karim Adiprasito, Marc Lackenby, Juan Souto +1
We describe a construction that takes as input a graph and a basis for its first homology, and returns a triangulation of a 3-dimensional homology sphere. This makes precise an ide…
The unknotting number, hard unknot diagrams, and reinforcement learning
Taylor Applebaum, Sam Blackwell, Alex Davies +5
We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upp…
What makes a good feedforward computational graph?
Alex Vitvitskyi, João G. M. Araújo, Marc Lackenby +1
As implied by the plethora of literature on graph rewiring, the choice of computational graph employed by a neural network can make a significant impact on its downstream performan…