5 papers
Moving between 3-manifold triangulations is NP-hard
Stephan Tillmann, Anastasiia Tsvietkova
We show that \textsc{number of bistellar moves and sparse degree-two edge collapses for 3-sphere} is NP-hard. It follows that a similar problem for an arbitrary 3-manifold is NP-ha…
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…
Polynomial bounds for surfaces in cusped 3-manifolds
Jessica S. Purcell, Anastasiia Tsvietkova
It is natural to ask how many isotopy classes of embedded essential surfaces lie in a given 3-manifold. The first bounds on the number of such surfaces were exponential, using norm…
Polynomial algorithm for alternating link equivalence
Touseef Haider, Anastasiia Tsvietkova
Link equivalence up to isotopy in a 3-space is the problem that lies at the root of knot theory, and is important in 3-dimensional topology and geometry. We consider its restrictio…
Geometric structures and representations of knot groups from knot diagrams
Kathleen L. Petersen, Anastasiia Tsvietkova
We describe a new method of producing equations for the canonical component of representation variety of a knot group into . Unlike known methods, this one does…