Publications
 (With C. Maclachlan) Commensurability classes of arithmetic Kleinian groups and
their Fuchsian subgroups. Math. Proc. Camb. Phil. Soc. 102 (1987),
251–257.
 (With C. Maclachlan)
The arithmetic structure of tetrahedral groups of hyperbolic isometries.
Mathematika 36 (1990), 221–240.
 A note on tracefields
of Kleinian groups. Bull. London Math. Soc. 22 (1990), 349–352.
 Arithmeticity of
knot complements. J. London Math. Soc. 43 (1991), 171–184.
 Totally geodesic
surfaces in hyperbolic 3manifolds. Proc. Edinburgh Math. Soc.
34 (1991), 77–88.
 (With W. D. Neumann)
Amalgamation and the invariant tracefield of Kleinian groups.
Math. Proc. Camb. Phil. Soc. 109 (1991), 509–515.
 (With C. Maclachlan)
Parameterizing Fuchsian subgroups of Bianchi groups. Canadian
J. Math. 43 (1991), 158–181.
 Commensurability
and isospectrality of arithmetic hyperbolic 2 and 3manifolds.
Duke Math J. 65 (1992), 215–228.
 (With W. D. Neumann)
Arithmetic of hyperbolic manifolds. In TOPOLOGY '90, Proceedings
of the Research Semester in Low Dimensional Topology at Ohio State
University. De Gruyter Verlag (1992), 273–310.
 (With W. D. Neumann)
Notes on Adams' small volume orbifolds. In TOPOLOGY '90, Proceedings
of the Research Semester in Low Dimensional Topology at Ohio State
University. De Gruyter Verlag (1992), 311–314.
 (With W. Menasco)
Totally geodesic surfaces in hyperbolic link complements. In TOPOLOGY
'90, Proceedings of the Research Semester in Low Dimensional Topology
at Ohio State University. De Gruyter Verlag (1992), 215–226.
 Some remarks on 2generator
hyperbolic 3manifolds. In Discrete Groups and Geometry, Proceedings
in honour of the retirement of A. M. Macbeath. L. M. S. Lecture
Note Series 173 (1992), 209–219.
 (With W. D. Neumann)
Rigidity of cusps in deformations of hyperbolic 3orbifolds. Math.
Ann. 295 (1993), 223237.
 (With D. D. Long) Closed incompressible surfaces in 2generator hyperbolic
3manifolds with a single cusp. Proc. Edinburgh Math. Soc. 36
(1993), 501–513.
 (With T. Chinburg)
Closed hyperbolic 3manifolds whose closed geodesics all are simple.
J. Diff. Geom. 38 (1993), 545–558.
 (With C. Adams) QuasiFuchsian surfaces in hyperbolic knot complements. Journal
Australian Math. Soc. 55 (1993), 116–131.
 (With K. N. Jones) Nonsimple closed geodesics in hyperbolic 3manifolds. Math.
Proc. Camb. Phil. Soc. 116 (1994), 339–351.
 (With D. Cooper
and D. D. Long) Bundles and finite foliations. Invent. Math.
118 (1994), 255–283.
 (With B. Bowditch
and C. Maclachlan) Arithmetic hyperbolic surface bundles.
Math. Annalen 302 (1995), 31–60.
 A nonHaken hyperbolic
3manifold covered by a surface bundle.Pacific J. Math. 167 (1995),
163–182.
 (With C. McA.
Gordon) Tangle decompositions of tunnel number one knots
and links. Journal of Knot Theory and its Ramifications 4 (1995),
389–409.
 (With C. Adams) Unknotting
tunnels in twobridge knot and link complements. Comment. Math.
Helv. 71 (1996), 617–627.
 (With D. D. Long
and C. Maclachlan) Splitting groups of signature (1;n). J.
Algebra 185 (1996), 329–341. (pdf)
 (With J. W. Anderson) Commensurability of Fuchsian groups and their axes. Proc.
A. M. S. 125 (1997), 941–942. (pdf)
 (With D. Cooper
and D. D. Long) Finite foliations and similarity interval
exchange maps. Topology 36 (1997), 209–227. (pdf)
 (With D. Cooper
and D. D. Long) Essential closed surfaces in bounded 3manifolds.
Journal of The American Math. Soc. 10, (1997), 553–563.
(pdf)
 (With F. W. Gehring,
C. Maclachlan and G. J. Martin) Arithmeticity, Discreteness
and Volume. Trans. A. M. S. 349 (1997), 3611–3643. (pdf)
 (With C. Maclachlan) Generalised Fibonacci Manifolds. J. of Transformation Groups,
2 (1997), 165–182.
 (With K. N. Jones)
Geodesic intersections in arithmetic hyperbolic 3manifolds. Duke
Math. J. 89 (1997), 75–86.
 (With C. Maclachlan) Invariant tracefields and quaternion algebras of polyhedral
groups. J. London Math. Soc. 58 (1998), 709–722. (pdf)
 (With D. D. Long) Simple quotients of hyperbolic 3manifold groups. Proc. A.
M. S. 126 (1998), 877–880. (pdf)
 (With D. D. Long) On Fuchsian groups with the same set of axes. Bull. London
Math. Soc. 30 (1998), 533 – 538. (pdf)
 (With D. D. Long)
Free products with amalgamation and padic Lie Groups, Canadian
Math. Bulletin, 41 (1998), 423–433.
 (With D. Cooper
and D. D. Long) Infinite Coxeter groups are virtually indicable.
Proc. Edinburgh Math. Soc. 41 (1998), 303–313.
 (With K. N. Jones)
Minimal index torsionfree subgroups in Kleinian groups. Math.
Annalen 310 (1998), 235–250. (pdf)
 (With P. Callahan)
Hyperbolic structures on knot complements. Chaos, Solitons and
Fractals 9 (1998), 705–738. (pdf)
 (With S. Wang) NonHaken 3manifolds are not large with respect to mappings
of nonzero degree. Communications in Analysis and Geometry, 7
(1999) 105–132
 (With D. D. Long)
Commensurability and the character variety, Math. Research Letters
6 (1999), 581–591. (pdf)
 (With D. D. Long)
On the geometric boundaries of hyperbolic 4manifolds, Geometry
and Topology, 4 (2000), 171–178. (pdf)
 (With C. Adams)
Systoles of hyperbolic 3manifolds. Math. Proc. Cambridge Philos.
Soc. 128 (2000), 103–110. (pdf)
 (With K. N. Jones)
Vol3 and other exceptional hyperbolic 3manifolds, Proc. Amer.
Math. Soc. 129 (2001), 2175–2185. (pdf)
 (With D. D. Long)
The fundamental group of the double of the figure eight knot exterior
is GFERF, Bull. London Math. Soc. 33 (2001), 391–396.
 (With D. D. Long)
Constructing hyperbolic manifolds which bound geometrically, Math.
Research Letters 8 (2001), 443–456. (pdf)
 (With D. D. Long) On subgroup separability in hyperbolic Coxeter groups, Geometriae
Dedicata, 87 (2001), 245–260. (pdf)
 (With I. Agol
and D. D. Long) The Bianchi groups are separable on geometrically
finite subgroups, Annals of Math. 153 (2001), 599–621. (pdf)
 (With T. Chinburg,
E. Friedman and K. N. Jones) The smallest volume arithmetic
hyperbolic 3manifold, Annali della Scuola Normale Superiore di
Pisa 30 (2001), 1–40.
 (With D. D. Long)
All flat manifolds are cusps of hyperbolic orbifolds, Algebraic
and Geometric Topology 2 (2002), 285–296. (pdf)
 (With D. D. Long)
Pseudomodular surfaces, Journal für de Reine Angew. 552 (2002),
77–100. (pdf)
 (With S. Wang
and Q. Zhou) Generalized Hopfian property, a minimal Haken
manifold and epimorphisms between 3manifold groups, Acta Mathematica
Sinica, English Series 18 (2002), 157–172. (pdf)
 (With C. Leininger)
The corank conjecture for 3manifold groups, Algebraic and Geometric
Topology 2 (2002), 37–50. (pdf)
 (With M. D. Baker) Arithmetic knots in closed 3manifolds, in Proceedings of
Knots 2000, J. Knot Theory and its Ramifications 11 (2002), 903–920.
(pdf)
 (With D. D. Long)
Integral points on character varieties, Math. Annalen. 325 (2003),
299–321. (pdf)
 (With E. Hamilton)
Eigenvalue fields of hyperbolic orbifolds, Proc. A. M. S. 132
(2004), 2497–2503. (pdf)
 (With C. McA.
Gordon and D. D. Long)
Surface subgroups of Coxeter and Artin groups, J. Pure and Applied
Algebra 189 (2004), 135–148. (pdf)
 (With D. D. Long)
Generalized Dedekind sums, Geometry and Topology Monographs 7,
Proceedings of the Casson Fest (2004), 205–212. (pdf)
 (With D. D. Long)
On asymmetric hyperbolic manifolds, Math. Proc. Camb. Phil. Soc.138
(2005), 301–306. (pdf)
 (With C. Leininger)
A combination theorem for Veech subgroups of the Mapping class
group, GAFA 16 (2006), 403–436. (pdf)
 Surface subgroups
of Mapping Class groups, in Problems about Mapping Class Groups,
Proc. Symp. Pure and Applied Math., ed. B. Farb. (2006), 274–286.
(pdf)
 (With D. D. Long
and C. Maclachlan) Arithmetic Fuchsian groups of genus zero.
Pure and Applied Math Quarterly 2 (2006), a special issue to celebrate
the 60th birthday of Professor J. H. Coates, 569–599. (pdf)
 (With D. Cooper
and D. D. Long) On the virtual Betti numbers of arithmetic
hyperbolic 3–manifolds, Geometry and Topology 11 (2007)
2265–2276. (pdf)
 The geometry and topology
of arithmetic hyperbolic 3manifolds, Proc. Symposium Topology,
Complex Analysis and Arithmetic of Hyperbolic Spaces, Kyoto 2006,
RIMS Kokyuroku Series, 1571 (2007), 31–58. (pdf)
 (With D. D. Long
and A. Lubotzky), Heegaard genus and Property
for hyperbolic 3manifolds, Journal of Topology 1 (2008) 152–158.
(pdf)
 (With D. D. Long) Subgroup separability and virtual retractions of groups,
Topology 47 (2008), 137–159. (pdf)
 (With D. D. Long)
Finding fibre faces in finite covers, Math Research Letters 15
(2008), 521–524. (pdf)
 (With G. S. Walsh)
Commensurability classes of 2bridge knot complements, Algebraic
and Geometric Topology 8 (2008), 1031–1057(pdf)
 (With T. Chinburg,
E. Hamilton and D. D. Long) Geodesics and
commensurability classes of arithmetic hyperbolic 3manifolds,
Duke Math. J. 145 (2008), 25–44.(pdf)
 (With C. Leininger,
D. B. McReynolds and W. D. Neumann) Length and eigenvalue
equivalence, International Math. Research Notices, volume 2007,
article ID rnm135, 24 pages, doi:10.1093/imrn/rnm135. (pdf)
 (With M. Lackenby
and D. D. Long) Covering spaces of arithmetic 3orbifolds,
International Math. Research Notices, volume 2008, article ID
rnn036, 38 pages, doi: 10.1093/imrn/rnn036. (pdf)
 (With M. Lackenby
and D. D. Long) LERF and the LubotzkySarnak Conjecture,
Geometry and Topology 12 (2008), 2047–2056(pdf)
 (With T. Chinburg
and D. D. Long) Cusps of minimal noncompact arithmetic hyperbolic
3orbifolds, Pure and Applied Math Quarterly 4 (2008), 1013–1031.
A special issue to celebrate the 80^{th} birthday of Professor
JP. Serre. (pdf)
 (With P. BonfertTaylor,
G. Martin and E. Taylor) Teichmüller mappings, quasiconformal
homogeneity, and nonamenable covers of Riemann surfaces, Pure Appl. Math. Q. 7 (2011), 455–468. A special issue to celebrate the 80^{th} birthday of F. W. Gehring. (pdf)
 (With D. D. Long),
Eigenvalues of hyperbolic elements in Kleinian
groups, In the tradition of Ahlfors–Bers V, Contemp. Math. 510, 197–208, A.M.S. Publications, (2010). (pdf)
 (With M. Boileau,
S. Boyer and S. Wang) Simon's Conjecture for 2bridge
knots in Communications in Analysis and Geometry 18 (2010), 121–143.
(pdf)
 (With D. D. Long), Grothendieck's problem for 3manifold groups in Groups, Geometry and Dynamics, 5 (2011), 479–499. (pdf)
 (With D. D. Long and M. Thistlethwaite), Zariski dense surface subgroups in SL(3,Z), Geometry and Topology 15 (2011), 1–9. (pdf)
 (With C. J. Leininger and D. D. Long) Commensurators of finitely generated nonfree Kleinian groups, Algebraic and Geometric Topology, 11 (2011), 605–624. (pdf)
 (With D. D. Long), Fields of definition of canonical curves, Interactions between hyperbolic geometry, quantum topology and number theory, Contemporary Math. 541, 247–257, A.M.S. Publications, (2011). (pdf)
 (With D. D. Long), Small subgroups of SL(3,Z), Experimental Math. 20 (2011), 412–425. (pdf)
 (With G. Masbaum) All finite groups are involved in Mapping Class groups, Geometry and Topology 12 (2012), 1393–1411. (pdf)
 (With M. D. Baker) Restricting the topology of 1–cusped arithmetic 3–manifolds, Algebraic & Geometric Topology 13 (2013) 1273–1298. (pdf)
 (With D. D. Long) Constructing thin subgroups of SL(4, R). International Math. Research Notices, volume 2013, article ID rns281, 11 pages,
doi:10.1093/imrn/rns281(pdf)
 (With D. D. Long) Constructing thin groups, MSRI Proceedings of the Hot Topics Workshop Thin Groups and Superstrong Approximation 151166. (pdf)
 (With D. B. McReynolds and M. Stover) Collisions at infinity in hyperbolic manifolds, Math. Proc. Camb. Phil. Soc. 155 (2013), 459–463 (pdf)
 (With D. B. McReynolds)
The genus spectrum of hyperbolic 3manifolds, Math. Research Letters 21 (2014), 169–185. (pdf)
 (With M. D. Baker) Principal congruence link complements, Ann. Fac. Sci. Toulouse 23 (2014), 1063–1092(pdf)
 Traces, lengths, axes and commensurability, Ann. Fac. Sci. Toulouse 23 (2014), 1103–1118. (pdf)
 (With M. R. Bridson) Nilpotent completions of groups, Grothendieck pairs and four problems of Baumslag, Int. Math. Research Notices Volume 2015, 2111–2140, doi: 10.1093/imrn/rnt353 (pdf)
 Profinite properties of discrete groups, Proceedings
of Groups St Andrews 2013, L.M.S. Lecture Note Series 242 73–104,
Cambridge Univ. Press (2015). (pdf)
 (With G. Masbaum) Frattini and related subgroups of Mapping Class Groups), Proceedings of the Steklov Institute, 292 (2016), a special issue to celebrate the 75th birthday of V. P. Platonov, 143–152. (pdf)
 (With M.R. Bridson and M. Conder), Determining Fuchsian groups by their finite quotients, Israel J. Math, 214 (2016), 1–41. (pdf)
 (With D. D. Long) Thin surface subgroups in cocompact lattices in
SL(3,R), Illinois J. Math. 60 (2016), 39–53, a special issue to celebrate the work of Wolfgang Haken. (pdf)
 (With S. Garoufalidis) Constructing 1cusped isospectral nonisometric
hyperbolic 3manifolds, Journal of Topology and Analysis 10 (2018), 1–25. (pdf)
 (With M. D. Baker) Principal Congruence Links: Class number greater than 1, Experimental Math, 27 (2018), 395–413. (pdf)
 (With M. R. Bridson and H. Wilton) Profinite rigidty and surface bundles over
the circle. Bull. London Math. Soc. 49 (2017) 831–841 (pdf)
 Profinite rigidity, The Proceedings of the 2018 I.C.M. Rio De Janeiro, Vol. 2 1211–1234. (pdf)
 (With A. Kolpakov and L. Slavich) Embedding arithmetic hyperbolic manifolds, Math. Research Letters 25 (2018), 1305–1328. (pdf)
 (With M. D. Baker) Congruence link complements–a 3dimensional Rademacher Conjecture in Cohomology of Arithmetic Groups, Proceedings of the 66th Birthday Conference of Joachim Schwermer, 177–200, (2018). (pdf)
 (With D. B. McReynolds) Determining hyperbolic 3manifolds by their
surfaces,Proc A.M.S 147 (2019), 443–450. (pdf)
 (With C. J. Leininger) PseudoAnosov homeomorphisms not arising from branched covers, to appear Groups, Geometry and Dynamics. (pdf)
 (With D. D. Long) Sequences of high rank lattices of large systole containing a fixed genus surface group, New York J. Math 25 (2019), 145–155. (pdf)
 (With M. D. Baker and M. Goerner) All principal congruence link complements, J. Algebra 528 (2019), 497–504. (pdf)
 Technical Report: All principal congruence link groups (pdf)
 All known principal congruence links (pdf)
 (With A. Kolpakov and S. Riolo) Many cusped hyperbolic 3manifolds do not bound geometrically to appear Proc. A. M. S. (pdf)
 (With M. R. Bridson) Profinite rigidity, fibering and the figureeight knot, to appear in What's Next?: The Mathematical Legacy of William P. Thurston. (pdf)
 (With A. Kontorovich, D. D. Long and A. Lubotzky) WHAT IS... a Thin Group? Notices of the A.M.S. 66 (2019), 905–910. (pdf)
 (With D. D. Long) Virtually spinning hyperbolic manifolds, to appear Proc. Edinburgh Math. Soc. (pdf)
 (With K. L. Petersen) Gonality and genus of canonical components of character varieties, to appear in the Proceedings of the conference in honour of Steve Boyer. (pdf)
Preprints
 (With T. Chinburg and M. Stover) Azumaya algebras and canonical components. (pdf)
 (With M. R. Bridson, D. B. McReynolds and R. Spitler) Absolute profinite rigidity
and hyperbolic geometry. (pdf)
 (with J. Jung) Embedding closed totally geodesic surfaces in Bianchi orbifolds
In Progress
 (With C. Maclachlan and A. Salgueiro) Some remarks on group actions on hyperbolic 3manifolds.
 (With M. R. Bridson, D. B. McReynolds and R. Spitler) On the profinite rigidity of triangle groups.
 (With C. McA. Gordon and J. Nogueira) Planar surfaces and meridional
subgroups of knot groups.
Books
In the Tradition of AhlforsBers VII, Contemporary Math. 696 American Math. Soc. (2017). Coeditors: A. Basmajian and Y. Minsky.
In the Tradition of AhlforsBers VI, Contemporary Mathematics 590 American Mathematical Society (2013). Coeditors: U. Hamenstadt, R. Rodriguez, S. Rhode, and M. Wolf. (pdf)
Surface
Subgroups and Subgroup Separability in 3Manifold Topology,
With D. D. Long, Publicações Matemáticas
no IMPA, (2005) (pdf)
The Arithmetic
of Hyperbolic 3Manifolds, with C. Maclachlan, Graduate
Text in Math. 219, SpringerVerlag (2003)
TOPOLOGY
'90, Proceedings of the Research Semester in Low
Dimensional Topology at Ohio State University. CoEditors: B.
Apanasov, W. D. Neumann and L. Siebenmann, De Gruyter Verlag,
(1992)
Recent
Lectures
Three Lectures at the Workshop on Geometric topology in Cortona
June 4–10, 2017 at the Palazzone in Cortona. (pdf)
Lectures at 2018 NZMRI Summer Workshop in Algebra and Representation Theory, Nelson NZ, January 7–13, 2018.
Click here and scroll down for slides.
Profinite rigidity, 2018 ICM talk, Rio De Janeiro, August 2018. (pdf)
Swiss Mathematical Society Annual Meeting, Public Lecture, June 2018 (pdf)
