Related papers: Regular Tessellation Link Complements
A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are quarter-circles, but Tangles comprised of thirds and sixths…
We prove that any isomorphism between the profinite completions of the fundamental groups of two cusped finite-volume hyperbolic 3-manifolds is regular and peripheral regular. As an application, we show that the $A$-polynomial of prime…
Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups…
The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL $4$-manifolds with empty or connected boundary, called {\it semi-simple} and {\it weak semi-simple crystallizations},…
Motivated by a question of Neumann and Reid, we study whether Dehn fillings on all but one cusp of a hyperbolic link complement can produce infinite families of knot complements with hidden symmetries which geometrically converge to the…
In this paper we present a classical construction of the Hyperbolic structure of the complement of a link in the sense of Thurston for the particular case of the Borromean rings link. As this is nothing new, the aim of this paper is to…
Regular tesselations of space are characterized through their Schlafli symbols {p,q,r}, where each cell has regular p-gonal sides, q meeting at each vertex, and r meeting on each edge. Regular tesselations with symbols {p,3,3} all satisfy…
Recently, many structured tensors are defined and their properties are discussed in the literature. In this paper, we introduce a new class of structured tensors, called exceptionally regular tensor, which is relevant to the tensor…
An irreducible 3--manifold with torus boundary either is a Seifert fibered space or admits at most three lens space fillings according to the Cyclic Surgery Theorem. We examine the sharpness of this theorem by classifying the non-hyperbolic…
The paper bounds the number of tessellations with T-shaped vertices on a fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random…
We classify the normal subgroups K of the tetrahedral group Delta=[3,5,3]^+, the even subgroup of the Coxeter group Gamma=[3,5,3], with Delta/K isomorphic to a finite simple group L_2(q). We determine their normalisers N(K) in the isometry…
We consider the "intrinsic" symmetry group of a two-component link $L$, defined to be the image $\Sigma(L)$ of the natural homomorphism from the standard symmetry group $\MCG(S^3,L)$ to the product $\MCG(S^3) \cross \MCG(L)$. This group,…
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite…
For a topological space $X$ we study continuous maps $f : X\to \mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings. We…
We study higher-dimensional homological analogues of bond percolation on a square lattice and site percolation on a triangular lattice. By taking a quotient of certain infinite cell complexes by growing sublattices, we obtain finite cell…
A topological commutative ring is said to be rigid when for every set $X$, the topological dual of the $X$-fold topological product of the ring is isomorphic to the free module over $X$. Examples are fields with a ring topology, discrete…
Classical fully augmented links have explicit hyperbolic geometry, and have diagrams on the 2-sphere in the 3-sphere. We generalise to construct fully augmented links projected to the reflection surface of any 3-manifold obtained by…
When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse…
Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that…
A representation for compact 3-manifolds with non-empty non-spherical boundary via 4-colored graphs (i.e., 4-regular graphs endowed with a proper edge-coloration with four colors) has been recently introduced by two of the authors, and an…