1 citations · 1 across the 11 of their papers we have counts for
12 papers
Quasi-Fuchsian groups and complex realisations of -deformed real numbers
Alex Elzenaar
We relate the theory of -rational and -real numbers introduced by Morier-Genoud and Ovsienko to the classical theory of Kleinian groups and their Teichmüller spaces. This pro…
On rank two Kleinian groups with three parabolics
Alex Elzenaar
The free group of rank is the fundamental group of the genus handlebody . We study discrete representations of this group into s…
Expansion joints in hyperbolic manifolds
Alex Elzenaar
Deformations of hyperbolic manifolds through metrics with cone singularities along closed loops were first studied by Thurston as continuous realisations of Dehn fillings. Instead…
Peripheral subgroups of Kleinian groups
Alex Elzenaar
The conformal boundary of a hyperbolic -manifold is a union of Riemann surfaces. If any of these Riemann surfaces has a nontrivial Teichmüller space, then the hyperbolic met…
From disc patterns in the plane to character varieties of knot groups
Alex Elzenaar
Motivated by an experimental study of groups generated by reflections in planar patterns of tangent circles, we describe some methods for constructing and studying representation s…
Changing topological type of compression bodies through cone manifolds
Alex Elzenaar
Homeomorphism types of compression bodies form the vertices of a graph where two vertices are joined by an edge if one compression body is obtained by gluing a -handle onto the…
On Thin Heckoid and Generalised Triangle Groups in }
Alex Elzenaar, Gaven Martin, Jeroen Schillewaert
We provide a brief overview of our upcoming work identifying all the thin Heckoid groups in . Here we give a complete list of the thin generalised triangle…
Putatively optimal projective spherical designs with little apparent symmetry
Alex Elzenaar, Shayne Waldron
We give some new explicit examples of putatively optimal projective spherical designs. i.e., ones for which there is numerical evidence that they are of minimal size. These form co…
Bounding deformation spaces of Kleinian groups with two generators
A. Elzenaar, J. Gong, G. J. Martin +1
In this article we provide simple and provable bounds on the size and shape of the locus of discrete subgroups of $\mathsf{PSL}(2,\mathbb{C})\cong \operatorname{Isom}^+(\mathbb{H}^…
Concrete one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds
Alex Elzenaar, Gaven Martin, Jeroen Schillewaert
The Riley slice is arguably the simplest example of a moduli space of Kleinian groups; it is naturally embedded in , and has a natural coordinate system (introduced b…
The combinatorics of Farey words and their traces
Alex Elzenaar, Gaven Martin, Jeroen Schillewaert
We introduce a family of 3-variable "Farey polynomials" that are closely connected with the geometry and topology of -manifolds and orbifolds as they can be used to produce conc…
Approximations of the Riley slice
Alex Elzenaar, Gaven Martin, Jeroen Schillewaert
Adapting the ideas of L. Keen and C. Series used in their study of the Riley slice of Schottky groups generated by two parabolics, we explicitly identify `half-space' neighbourhood…