Related papers: Exotic components in linear slices of quasi-Fuchsi…

In this paper, we study the topology of the boundaries of quasi-Fuchsian spaces. We first show for a given convergent sequence of quasi-Fuchsian groups, how we can know the end invariant of the limit group from the information on the…

Let $P(S)$ be the space of projective structures on a closed surface $S$ of genus $g >1$ and let $Q(S)$ be the subset of $P(S)$ of projective structures with quasifuchsian holonomy. It is known that $Q(S)$ consists of infinitely many…

Semi-arithmetic Fuchsian groups is a wide class of discrete groups of isometries of the hyperbolic plane which includes arithmetic Fuchsian groups, hyperbolic triangle groups, groups admitting a modular embedding, and others. We introduce a…

Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…

Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…

After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the complex length l_V and the complex twist tau_V,W parameters define a holomorphic embedding of the quasifuchsian space QF of punctured tori into C^2. It is called…

We prove a converse theorem for the case of quasi-split non-split even special orthogonal groups over finite fields. There are two main difficulties which arise from the outer automorphism and non-split part of the torus. The outer…

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…

It is a classical result of Dal'Bo that the length spectrum of a non-elementary Fuchsian group is non-arithmetic, namely, it generates a dense additive subgroup of $\mathbb{R}$. In this note we provide an elementary proof of an extension of…

In this paper we give a complete description of the space $ \QF $ of quasifuchsian punctured torus groups in terms of what we call {\em pleating invariants}. These are natural invariants of the boundary $\bch$ of the convex core of the…

We consider a scenario in which the discrete weak symmetry between quarks and leptons is extended to the weak force by introducing exotic partners. We conjecture that there exists a hidden discrete symmetry $\tilde{P}$, defining a $Z_2$…

A question raised by Davies et al [Phys. Rev. Lett. 131, 2023] is: "Can developing new cut and project models, where the lattice is not square or the curve is non-linear, generate better performing graded metamaterials?" In this article, we…

We present classification results for exceptional Legendrian realisations of torus knots. These are the first results of that kind for non-trivial topological knot types. Enumeration results of Ding-Li-Zhang concerning tight contact…

We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on the A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is…

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building…

We consider finite 2-complexes X that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT(-1) metrics on X which are piecewise…

Gromov Hyperbolic groups have remarkable finiteness properties;for example those that are torsion-free are fundamental groups of finitecomplexes whose universal cover iscontractible (property~$F$). In this talk we will show thattheir…

An almost-Fuchsian group is a quasi-Fuchsian group such that the quotient hyperbolic manifold contains a closed incompressible minimal surface with principal curvatures contained in (-1,1). We show that the domain of discontinuity of an…

Gompf's end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$ topology, but for which the exotic differentiable structure is confined to a region which…

We consider quasifuchsian manifolds with "particles", i.e., cone singularities of fixed angle less than $\pi$ going from one connected component of the boundary at infinity to the other. Each connected component of the boundary at infinity…