Related papers: An algorithm to detect laminar 3-manifolds
0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation or M can be shown to be one of the…
We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal…
We consider the problem of detecting anomalies in the directional distribution of fibre materials observed in 3D images. We divide the image into a set of scanning windows and classify them into two clusters: homogeneous material and…
Recently, a system identification method based on center manifold is proposed to identify polynomial nonlinear systems with uncontrollable linearization. This note presents a numerical example to show the effectiveness of this method.
We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.
We prove that fundamental groups of orientable (geometrizable) 3-manifolds have a solvable conjugacy problem.
The non-existence of non-trivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is obtained. Furthermore, the isometry classes are examined.
In this paper we prove two results, one semi-historical and the other new. The semi-historical result, which goes back to Thurston and Riley, is that the geometrization theorem implies that there is an algorithm for the homeomorphism…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
We review the state of the art of the classification of real uniruled threefolds
We show that if a closed, oriented 3-manifold M is promised to be homeomorphic to a lens space L(n,k) with n and k unknown, then we can compute both n and k in polynomial time in the size of the triangulation of M. The tricky part is the…
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…
It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such…
Automatic detection and segmentation of overlapping leaves in dense foliage can be a difficult task, particularly for leaves with strong textures and high occlusions. We present Dense-Leaves, an image dataset with ground truth segmentation…
We prove that if two cusped hyperbolic $3$-manifolds admit a regular isomorphism between the profinite completions of their fundamental groups, then they share the same $A$-polynomial and their strongly detected boundary slopes match up.
We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of {\pi}/n. We find new substitution rules admitting 7-fold rotational symmetry at many different…
We use the computer algebra system Magma to study graded rings of Fano 3-folds of index >=3 in terms of their Hilbert series.
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…
We prove that every distinct covering system has a modulus divisible by either 2 or 3.