5 citations · 10 across the 13 of their papers we have counts for
18 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-vol…
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…
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…
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…
Standard position for surfaces in link complements in arbitrary 3-manifolds
Jessica S. Purcell, Anastasiia Tsvietkova
Since the 1980s, it has been known that essential surfaces in alternating link complements can be isotoped to be transverse to the link diagram almost everywhere, with the exceptio…