James W. Anderson
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
James W. Anderson has a total of 47 co-authors. Here are the top co-authors by number of shared publications:
Richard D. Canary
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA US
5 shared publications- Javier Aramayona
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
4 shared publications - Aaron Wootton
University of Portland
3 shared publications - Kenneth J. Shackleton3 shared publications
- Alexandra Pettet
Department of Mathematics, University of Michigan, Ann Arbor, USA
2 shared publications - Hugo Parlier
University of Luxembourg
2 shared publications
Latest Publications
- 1 August 2025
- Published by American Mathematical Society (AMS) in Notices of the American Mathematical Society
- Vol. 72 (07)
Bernard Maskit Memorial Tribute
- 1 August 2025
- Published by American Mathematical Society (AMS) in Notices of the American Mathematical Society
- Vol. 72 (07)
Bernard Maskit Memorial Tribute
- Open Access
- 4 September 2020
- Published by American Society for Engineering Education
- p. 23.1018.1-23.1018.12
RAPTOR - A Vehicle to Enhance Logical Thinking
- 4 September 2020
- Published by American Society for Engineering Education
- p. 23.1018.1-23.1018.12
Open AccessRAPTOR - A Vehicle to Enhance Logical Thinking
- 1 April 2016
- Published by Project MUSE in American Journal of Mathematics
- Vol. 138 (2) , 473-498
Relative shapes of thick subsets of moduli space
A closed hyperbolic surface of genus $g\ge 2$ can be decomposed into pairs of pants along shortest closed geodesics and if these curves are sufficiently short (and with lengths uniformly bounded away from $0$), then the geometry of the surface is essentially determined by the combinatorics of the pants decomposition. These combinatorics are determined by a trivalent graph, so we call such surfaces {\it trivalent}. In this paper, in a first attempt to understand the ``shape'' of the subset ${\bf X}_g$ of moduli space consisting of surfaces whose systoles fill, we compare it metrically, asymptotically in $g$, with the set ${\bf Y}_g$ of trivalent surfaces. As our main result, we find that the set ${\bf X}_g\cap{\bf Y}_g$ is metrically ``sparse'' in ${\bf X}_g$ (where we equip $({\cal M}_g$ with either the Thurston or the Teichm\"uller metric).- 1 April 2016
- Published by Project MUSE in American Journal of Mathematics
- Vol. 138 (2) , 473-498
Relative shapes of thick subsets of moduli space
A closed hyperbolic surface of genus $g\ge 2$ can be decomposed into pairs of pants along shortest closed geodesics and if these curves are sufficiently short (and with lengths uniformly bounded away from $0$), then the geometry of the surface is essentially determined by the combinatorics of the pants decomposition. These combinatorics are determined by a trivalent graph, so we call such surfaces {\it trivalent}. In this paper, in a first attempt to understand the ``shape'' of the subset ${\bf X}_g$ of moduli space consisting of surfaces whose systoles fill, we compare it metrically, asymptotically in $g$, with the set ${\bf Y}_g$ of trivalent surfaces. As our main result, we find that the set ${\bf X}_g\cap{\bf Y}_g$ is metrically ``sparse'' in ${\bf X}_g$ (where we equip $({\cal M}_g$ with either the Thurston or the Teichm\"uller metric).- Open Access
Prising apart geodesics by length in hyperbolic 3-manifolds
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 hyperbolic structures on the surface or 3-manifold completely determines the curve. For an orientable surface $S$ of negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case on closed surfaces of genus two that we describe completely), while for hyperbolizable 3-manifolds, we show that curves freely homotopic to simple curves on $\partial M$ have this property.Open AccessPrising apart geodesics by length in hyperbolic 3-manifolds
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 hyperbolic structures on the surface or 3-manifold completely determines the curve. For an orientable surface $S$ of negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case on closed surfaces of genus two that we describe completely), while for hyperbolizable 3-manifolds, we show that curves freely homotopic to simple curves on $\partial M$ have this property. - 1 January 2015
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 158 (3) , 547-572
Prising apart geodesics by length in hyperbolic manifolds
We develop a condition on a closed curve on a surface or in a 3-manifold that implies that the length function associated to the curve on the space of all hyperbolic structures on the surface or in the 3-manifold (respectively) completely determines the curve. Specifically, for an orientable surfaceSof negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case arising from hyperellipticity that we describe completely). For a large class of hyperbolizable 3-manifolds, we show that curves freely homotopic to simple curves on ∂Mhave this property.
- 1 January 2015
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 158 (3) , 547-572
Prising apart geodesics by length in hyperbolic manifolds
We develop a condition on a closed curve on a surface or in a 3-manifold that implies that the length function associated to the curve on the space of all hyperbolic structures on the surface or in the 3-manifold (respectively) completely determines the curve. Specifically, for an orientable surfaceSof negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case arising from hyperellipticity that we describe completely). For a large class of hyperbolizable 3-manifolds, we show that curves freely homotopic to simple curves on ∂Mhave this property.
- 14 June 2014
- Published by Springer Nature in Computational Methods and Function Theory
- Vol. 14 (2-3) , 453-464
Limit Set Intersection Theorems for Kleinian Groups and a Conjecture of Susskind
- 14 June 2014
- Published by Springer Nature in Computational Methods and Function Theory
- Vol. 14 (2-3) , 453-464
Limit Set Intersection Theorems for Kleinian Groups and a Conjecture of Susskind
- Open Access
- 12 February 2014
- Published by Springer Nature in Archiv der Mathematik
- Vol. 102 (2) , 181-190
Gaps in the space of skeletal signatures
- 12 February 2014
- Published by Springer Nature in Archiv der Mathematik
- Vol. 102 (2) , 181-190
Open AccessGaps in the space of skeletal signatures
- 25 November 2013
- Published by European Mathematical Society - EMS - Publishing House GmbH in Commentarii Mathematici Helvetici
- Vol. 88 (4) , 813-857
Strong convergence of Kleinian groups: the cracked eggshell
In this paper we give a complete description of the set \mathrm{SH}(\pi_1(M)) of discrete faithful representations of the fundamental group of a compact, orientable, hyperbolizable 3-manifold with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part of this description, we introduce coordinates on \mathrm{SH}(\pi_1(M)) that extend the usual Ahlfors–Bers coordinates. We use these coordinates to show the local connectivity of \mathrm{SH}(\pi_1(M)) and study the action of the modular group of M on \mathrm{SH}(\pi_1(M)) .
- 25 November 2013
- Published by European Mathematical Society - EMS - Publishing House GmbH in Commentarii Mathematici Helvetici
- Vol. 88 (4) , 813-857
Strong convergence of Kleinian groups: the cracked eggshell
In this paper we give a complete description of the set \mathrm{SH}(\pi_1(M)) of discrete faithful representations of the fundamental group of a compact, orientable, hyperbolizable 3-manifold with incompressible boundary, equipped with the strong topology, with the description given in term of the end invariants of the quotient manifolds. As part of this description, we introduce coordinates on \mathrm{SH}(\pi_1(M)) that extend the usual Ahlfors–Bers coordinates. We use these coordinates to show the local connectivity of \mathrm{SH}(\pi_1(M)) and study the action of the modular group of M on \mathrm{SH}(\pi_1(M)) .
- Open Access
Limit set intersection theorems for Kleinian groups and a conjecture of Susskind
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, and the intersection of the limit sets of the subgroups. Of specific interest is the extent to which the intersection of the limit sets being non-empty implies that the intersection of the subgroups is non-trivial. We present examples to show that a conjecture of Susskind, stating that the intersection of the sets of conical limit points of subgroups $\Phi$ and $\Theta$ of a Kleinian group $\Gamma$ is contained in the limit set of $\Phi\cap \Theta$, is as sharp as can reasonably be expected. We further show that Susskind's conjecture holds most of the time.Open AccessLimit set intersection theorems for Kleinian groups and a conjecture of Susskind
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, and the intersection of the limit sets of the subgroups. Of specific interest is the extent to which the intersection of the limit sets being non-empty implies that the intersection of the subgroups is non-trivial. We present examples to show that a conjecture of Susskind, stating that the intersection of the sets of conical limit points of subgroups $\Phi$ and $\Theta$ of a Kleinian group $\Gamma$ is contained in the limit set of $\Phi\cap \Theta$, is as sharp as can reasonably be expected. We further show that Susskind's conjecture holds most of the time. - Open Access
Gaps in the space of skeletal signatures
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--35.] as a tool to describe the space of all signatures with which a group can act on a surface of genus $\sigma \geq 2$. In the present paper we provide a complete description of the gaps that appear in the space of skeletal signatures, together with proofs of the conjectures posed in our earlier work.Open AccessGaps in the space of skeletal signatures
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--35.] as a tool to describe the space of all signatures with which a group can act on a surface of genus $\sigma \geq 2$. In the present paper we provide a complete description of the gaps that appear in the space of skeletal signatures, together with proofs of the conjectures posed in our earlier work.