33 citations · 168 across the 48 of their papers we have counts for
44 papers · 1 filter
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(…
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…
Recognising elliptic manifolds
Marc Lackenby, Saul Schleimer
We show that the problem of deciding whether a closed three-manifold admits an elliptic structure lies in NP. Furthermore, determining the homeomorphism type of an elliptic manifol…
The signature and cusp geometry of hyperbolic knots
Alex Davies, András Juhász, Marc Lackenby +1
We introduce a new real-valued invariant called the natural slope of a hyperbolic knot in the 3-sphere, which is defined in terms of its cusp geometry. We show that twice the knot…
The computational complexity of knot genus in a fixed 3-manifold
Marc Lackenby, Mehdi Yazdi
We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manifold bounds a surface of genus at most is in co-NP. This answers a question o…