Alan Reid, Professor of Mathematics at the University of Texas
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Publications

  1. (With C. Maclachlan) Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups. Math. Proc. Camb. Phil. Soc. 102 (1987), 251–257.
  2. (With C. Maclachlan) The arithmetic structure of tetrahedral groups of hyperbolic isometries. Mathematika 36 (1990), 221–240.
  3. A note on trace-fields of Kleinian groups. Bull. London Math. Soc. 22 (1990), 349–352.
  4. Arithmeticity of knot complements. J. London Math. Soc. 43 (1991), 171–184.
  5. Totally geodesic surfaces in hyperbolic 3-manifolds. Proc. Edinburgh Math. Soc. 34 (1991), 77–88.
  6. (With W. D. Neumann) Amalgamation and the invariant trace-field of Kleinian groups. Math. Proc. Camb. Phil. Soc. 109 (1991), 509–515.
  7. (With C. Maclachlan) Parameterizing Fuchsian subgroups of Bianchi groups. Canadian J. Math. 43 (1991), 158–181.
  8. Commensurability and isospectrality of arithmetic hyperbolic 2 and 3-manifolds. Duke Math J. 65 (1992), 215–228.
  9. (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.
  10. (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.
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  12. (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.
  13. Some remarks on 2-generator hyperbolic 3-manifolds. 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.
  14. (With W. D. Neumann) Rigidity of cusps in deformations of hyperbolic 3-orbifolds. Math. Ann. 295 (1993), 223-237.
  15. (With D. D. Long) Closed incompressible surfaces in 2-generator hyperbolic 3-manifolds with a single cusp. Proc. Edinburgh Math. Soc. 36 (1993), 501–513.
  16. (With T. Chinburg) Closed hyperbolic 3-manifolds whose closed geodesics all are simple. J. Diff. Geom. 38 (1993), 545–558.
  17. (With C. Adams) Quasi-Fuchsian surfaces in hyperbolic knot complements. Journal Australian Math. Soc. 55 (1993), 116–131.
  18. (With K. N. Jones) Non-simple closed geodesics in hyperbolic 3-manifolds. Math. Proc. Camb. Phil. Soc. 116 (1994), 339–351.
  19. (With D. Cooper and D. D. Long) Bundles and finite foliations. Invent. Math. 118 (1994), 255–283.
  20. (With B. Bowditch and C. Maclachlan) Arithmetic hyperbolic surface bundles. Math. Annalen 302 (1995), 31–60.
  21. A non-Haken hyperbolic 3-manifold covered by a surface bundle.Pacific J. Math. 167 (1995), 163–182.
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  23. (With C. McA. Gordon) Tangle decompositions of tunnel number one knots and links. Journal of Knot Theory and its Ramifications 4 (1995), 389–409.
  24. (With C. Adams) Unknotting tunnels in two-bridge knot and link complements. Comment. Math. Helv. 71 (1996), 617–627.
  25. (With D. D. Long and C. Maclachlan) Splitting groups of signature (1;n). J. Algebra 185 (1996), 329–341. (pdf)
  26. (With J. W. Anderson) Commensurability of Fuchsian groups and their axes. Proc. A. M. S. 125 (1997), 941–942. (pdf)
  27. (With D. Cooper and D. D. Long) Finite foliations and similarity interval exchange maps. Topology 36 (1997), 209–227. (pdf)
  28. (With D. Cooper and D. D. Long) Essential closed surfaces in bounded 3-manifolds. Journal of The American Math. Soc. 10, (1997), 553–563. (pdf)
  29. (With F. W. Gehring, C. Maclachlan and G. J. Martin) Arithmeticity, Discreteness and Volume. Trans. A. M. S. 349 (1997), 3611–3643. (pdf)
  30. (With C. Maclachlan) Generalised Fibonacci Manifolds. J. of Transformation Groups, 2 (1997), 165–182.
  31. (With K. N. Jones) Geodesic intersections in arithmetic hyperbolic 3-manifolds. Duke Math. J. 89 (1997), 75–86.
  32. (With C. Maclachlan) Invariant trace-fields and quaternion algebras of polyhedral groups. J. London Math. Soc. 58 (1998), 709–722. (pdf)
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  34. (With D. D. Long) Simple quotients of hyperbolic 3-manifold groups. Proc. A. M. S. 126 (1998), 877–880. (pdf)
  35. (With D. D. Long) On Fuchsian groups with the same set of axes. Bull. London Math. Soc. 30 (1998), 533 – 538. (pdf)
  36. (With D. D. Long) Free products with amalgamation and p-adic Lie Groups, Canadian Math. Bulletin, 41 (1998), 423–433.
  37. (With D. Cooper and D. D. Long) Infinite Coxeter groups are virtually indicable. Proc. Edinburgh Math. Soc. 41 (1998), 303–313.
  38. (With K. N. Jones) Minimal index torsion-free subgroups in Kleinian groups. Math. Annalen 310 (1998), 235–250. (pdf)
  39. (With P. Callahan) Hyperbolic structures on knot complements. Chaos, Solitons and Fractals 9 (1998), 705–738. (pdf)
  40. (With S. Wang) Non-Haken 3-manifolds are not large with respect to mappings of non-zero degree. Communications in Analysis and Geometry, 7 (1999) 105–132
  41. (With D. D. Long) Commensurability and the character variety, Math. Research Letters 6 (1999), 581–591. (pdf)
  42. (With D. D. Long) On the geometric boundaries of hyperbolic 4-manifolds, Geometry and Topology, 4 (2000), 171–178. (pdf)
  43. (With C. Adams) Systoles of hyperbolic 3-manifolds. Math. Proc. Cambridge Philos. Soc. 128 (2000), 103–110. (pdf)
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  45. (With K. N. Jones) Vol3 and other exceptional hyperbolic 3-manifolds, Proc. Amer. Math. Soc. 129 (2001), 2175–2185. (pdf)
  46. (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.
  47. (With D. D. Long) Constructing hyperbolic manifolds which bound geometrically, Math. Research Letters 8 (2001), 443–456. (pdf)
  48. (With D. D. Long) On subgroup separability in hyperbolic Coxeter groups, Geometriae Dedicata, 87 (2001), 245–260. (pdf)
  49. (With I. Agol and D. D. Long) The Bianchi groups are separable on geometrically finite subgroups, Annals of Math. 153 (2001), 599–621. (pdf)
  50. (With T. Chinburg, E. Friedman and K. N. Jones) The smallest volume arithmetic hyperbolic 3-manifold, Annali della Scuola Normale Superiore di Pisa 30 (2001), 1–40.
  51. (With D. D. Long) All flat manifolds are cusps of hyperbolic orbifolds, Algebraic and Geometric Topology 2 (2002), 285–296. (pdf)
  52. (With D. D. Long) Pseudomodular surfaces, Journal für de Reine Angew. 552 (2002), 77–100. (pdf)
  53. (With S. Wang and Q. Zhou) Generalized Hopfian property, a minimal Haken manifold and epimorphisms between 3-manifold groups, Acta Mathematica Sinica, English Series 18 (2002), 157–172. (pdf)
  54. (With C. Leininger) The co-rank conjecture for 3-manifold groups, Algebraic and Geometric Topology 2 (2002), 37–50. (pdf)
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  56. (With M. D. Baker) Arithmetic knots in closed 3-manifolds, in Proceedings of Knots 2000, J. Knot Theory and its Ramifications 11 (2002), 903–920. (pdf)
  57. (With D. D. Long) Integral points on character varieties, Math. Annalen. 325 (2003), 299–321. (pdf)
  58. (With E. Hamilton) Eigenvalue fields of hyperbolic orbifolds, Proc. A. M. S. 132 (2004), 2497–2503. (pdf)
  59. (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)
  60. (With D. D. Long) Generalized Dedekind sums, Geometry and Topology Monographs 7, Proceedings of the Casson Fest (2004), 205–212. (pdf)
  61. (With D. D. Long) On asymmetric hyperbolic manifolds, Math. Proc. Camb. Phil. Soc.138 (2005), 301–306. (pdf)
  62. (With C. Leininger) A combination theorem for Veech subgroups of the Mapping class group, GAFA 16 (2006), 403–436. (pdf)
  63. 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)
  64. (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)
  65. (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)
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  67. The geometry and topology of arithmetic hyperbolic 3-manifolds, Proc. Symposium Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces, Kyoto 2006, RIMS Kokyuroku Series, 1571 (2007), 31–58. (pdf)
  68. (With D. D. Long and A. Lubotzky), Heegaard genus and Property for hyperbolic 3-manifolds, Journal of Topology 1 (2008) 152–158. (pdf)
  69. (With D. D. Long) Subgroup separability and virtual retractions of groups, Topology 47 (2008), 137–159. (pdf)
  70. (With D. D. Long) Finding fibre faces in finite covers, Math Research Letters 15 (2008), 521–524. (pdf)
  71. (With G. S. Walsh) Commensurability classes of 2-bridge knot complements, Algebraic and Geometric Topology 8 (2008), 1031–1057(pdf)
  72. (With T. Chinburg, E. Hamilton and D. D. Long) Geodesics and
    commensurability classes of arithmetic hyperbolic 3-manifolds, Duke Math. J. 145 (2008), 25–44.(pdf)
  73. (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)
  74. (With M. Lackenby and D. D. Long) Covering spaces of arithmetic 3-orbifolds, International Math. Research Notices, volume 2008, article ID rnn036, 38 pages, doi: 10.1093/imrn/rnn036. (pdf)
  75. (With M. Lackenby and D. D. Long) LERF and the Lubotzky-Sarnak Conjecture, Geometry and Topology 12 (2008), 2047–2056(pdf)
  76. (With T. Chinburg and D. D. Long) Cusps of minimal non-compact arithmetic hyperbolic 3-orbifolds, Pure and Applied Math Quarterly 4 (2008), 1013–1031. A special issue to celebrate the 80th birthday of Professor J-P. Serre. (pdf)
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  78. (With P. Bonfert-Taylor, G. Martin and E. Taylor) Teichmüller mappings, quasi-conformal homogeneity, and non-amenable covers of Riemann surfaces, Pure Appl. Math. Q. 7 (2011), 455–468. A special issue to celebrate the 80th birthday of F. W. Gehring. (pdf)
  79. (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)
  80. (With M. Boileau, S. Boyer and S. Wang) Simon's Conjecture for 2-bridge
    knots in Communications in Analysis and Geometry 18 (2010), 121–143. (pdf)
  81. (With D. D. Long), Grothendieck's problem for 3-manifold groups in Groups, Geometry and Dynamics, 5 (2011), 479–499. (pdf)
  82. (With D. D. Long and M. Thistlethwaite), Zariski dense surface subgroups in SL(3,Z), Geometry and Topology 15 (2011), 19. (pdf)
  83. (With C. J. Leininger and D. D. Long) Commensurators of finitely generated non-free Kleinian groups, Algebraic and Geometric Topology, 11 (2011), 605624. (pdf)
  84. (With D. D. Long), Fields of definition of canonical curves, Interactions between hyperbolic geometry, quantum topology and number theory, Contemporary Math. 541, 247257, A.M.S. Publications, (2011). (pdf)
  85. (With D. D. Long), Small subgroups of SL(3,Z), Experimental Math. 20 (2011), 412425. (pdf)
  86. (With G. Masbaum) All finite groups are involved in Mapping Class groups, Geometry and Topology 12 (2012), 13931411. (pdf)
  87. (With M. D. Baker) Restricting the topology of 1cusped arithmetic 3manifolds, Algebraic & Geometric Topology 13 (2013) 1273–1298. (pdf)
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  89. (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)
  90. (With D. D. Long) Constructing thin groups, MSRI Proceedings of the Hot Topics Workshop Thin Groups and Super-strong Approximation 151-166. (pdf)
  91. (With D. B. McReynolds and M. Stover) Collisions at infinity in hyperbolic manifolds, Math. Proc. Camb. Phil. Soc. 155 (2013), 459–463 (pdf)
  92. (With D. B. McReynolds) The genus spectrum of hyperbolic 3-manifolds, Math. Research Letters 21 (2014), 169--185. (pdf)
  93. (With M. R. Bridson) Nilpotent completions of groups, Grothendieck pairs and four problems of Baumslag, to appear Int. Math. Research Notices (pdf)
  94. Traces, lengths, axes and commensurability. To appear Ann. Fac. Sci. Toulouse. (pdf)
  95. (With M.R. Bridson and M. Conder), Determining Fuchsian groups by their finite quotients,to appear Israel J. Math. (pdf)
  96. (With M. D. Baker) Principal congruence link complements, to
    appear Ann. Fac. Sci. Toulouse. (pdf)

 

Preprints

  • Profinite properties of discrete groups. (pdf)
  • (With K. L. Petersen) Gonality and genus of canonical components of character varieties. (pdf)

In Progress

  • (With C. Maclachlan and A. Salgueiro), Some remarks on group actions on hyperbolic 3-manifolds.
  • (With S. Garoufalidis) Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds.

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Books

In the Tradition of Ahlfors-Bers VI, Contemporary Mathematics 590 American Mathematical Society (2013). Co-editors: U. Hamenstadt, R. Rodriguez, S. Rhode, and M. Wolf. (pdf)

Surface Subgroups and Subgroup Separability in 3-Manifold Topology, with D. D. Long, Publicações Matemáticas no IMPA, (2005) (pdf)

The Arithmetic of Hyperbolic 3-Manifolds, with C. Maclachlan, Graduate Text in Math. 219, Springer-Verlag (2003)

TOPOLOGY '90, Proceedings of the Research Semester in Low Dimensional Topology at Ohio State University. Co-Editors: B. Apanasov, W. D. Neumann and L. Siebenmann, De Gruyter Verlag, (1992)

 

Recent Lectures

Transparencies from lectures at a Summer School in Pleinfeld Germany, Sept 2006. Part of the International Research Training Group in Arithmetic and Geometry (Humboldt University (Berlin), University of Zurich and ETH Zurich).

Transparencies Group Theory, Number Theory, and Geometry, Conference on occasion of Fritz Grunewald's 60th birthday, Oxford University, April 2009.

Notes taken from a series of 3 lectures at Hyperbolic geometry:
algorithmic, number theoretic and numerical aspects
, KIAS Seoul, South Korea, March 2010.

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