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math.GT2026
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-vo…
math.GT2026
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(…
math.GT2025
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…