189 citations · 218 across the 19 of their papers we have counts for
13 papers · 1 filter
Omnipersistent signatures
James W. Anderson, Aaron Wootton
In this note, we lay the groundwork for a new approach to the problem of group-signature classification of group actions on closed Riemann surfaces. This new approach first focuses…
Limit set intersection theorems for Kleinian groups and a conjecture of Susskind
James W Anderson
We continue here the investigation of the relationship between the intersection of a pair of subgroups of a Kleinian group, and in particular the limit set of that intersection, an…
Gaps in the space of skeletal signatures
James W Anderson, Aaron Wootton
Skeletal signatures were introduced in [J W Anderson and A Wootton, A Lower Bound for the Number of Group Actions on a Compact Riemann Surface, Algebr. Geom. Topol. 12 (2012) 19--3…
Relative shapes of thick subsets of moduli space
James W. Anderson, Hugo Parlier, Alexandra Pettet
A closed hyperbolic surface of genus can be decomposed into pairs of pants along shortest closed geodesics and if these curves are sufficiently short (and with lengths uni…
Prising apart geodesics by length in hyperbolic 3-manifolds
James W. Anderson
In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyp…
Strong convergence of Kleinian groups: the cracked eggshell
James W. Anderson, Cyril Lecuire
In this paper we give a complete description of the set of discrete faithful representations SH(M) uniformizing a compact, orientable, hyperbolizable 3-manifold M with incompressib…
Small filling sets of curves on a surface
James W. Anderson, Hugo Parlier, Alexandra Pettet
We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus which fill and pairwise intersect at most $K\g…
A simple criterion for non-relative hyperbolicity and one-endedness of groups
James W. Anderson, Javier Aramayona, Kenneth J. Shackleton
We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many importa…
Commensurability and locally free Kleinian groups
James W. Anderson
We show that there exist infinitely many commensurability classes of finite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup which is locally free but not…
Cores of hyperbolic 3-manifolds and limits of Kleinian groups II
James W. Anderson, Richard D. Canary
Troels Jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic Kleinian groups agree if there are no new parabolics in t…
The visual core of a hyperbolic 3-manifold
James W. Anderson, Richard D. Canary
We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the c…
A brief survey of the deformation theory of Kleinian groups
James W. Anderson
We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kle…
The topology of deformation spaces of Kleinian groups
James W. Anderson, Richard D. Canary, Darryl McCullough
Let M be a compact, hyperbolizable 3-manifold with nonempty incompressible boundary and let AH(π_1(M)) denote the space of (conjugacy classes of) discrete faithful representations…