6 papers
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…
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}^…
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…
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 me…
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…