Publications - D. D. Long

A preprint accessible below may differ somewhat from its final published version, in particular some of the earlier papers may be without their figures. Preprints are in .pdf format and so may be read using the free Acrobat Reader.
  1. Strongly plus amphicheiral knots are algebraically slice. Math. Proc. Camb. Phil. Soc. vol. 95 (1984), pp. 309 - 312.

  2. Planar kernels in surface groups. Oxford Quart. J. of Math. vol. 35 (1984), pp. 305 - 310.

  3. (with A. J. Casson) Algorithmic compression of surface automorphisms. Inventiones Math. vol. 81 (1985), pp. 295 - 303.
  4. A note on the normal subgroups of mapping class groups. Math. Proc. Camb. Phil. Soc. vol. 99 (1986), pp. 295 - 303.

  5. Constructing pseudo-Anosov maps.Knots and manifolds. Ed. D. Rolfsen. Springer-Verlag Lecture Notes No. 1144, pp. 108 - 114.

  6. Discs in compression bodies. Pacific Journal of Math. vol. 122 (1986), pp. 129 - 146.

  7. (with H. R. Morton) Hyperbolic 3-manifolds and surface automorphisms. Topology vol. 25 (1986), pp. 575 - 583.

  8. (with S. Kojima)Virtual Betti numbers of some hyperbolic manifolds. A Fete of Topology. Ed. Y. Matsumoto et al. Academic Press, pp. 417 - 437.

  9. Maximal subgroups in mapping class groups. Preprint.

  10. Immersions and embeddings of totally geodesic surfaces. Bulletin London Math. Society vol. 19 (1987), pp. 481 - 484.

  11. (with S. P. Humphries) On the Mal'cev quotients of certain hyperbolic link groups. Math. Proc. Camb. Phil. Soc. vol. 102 (1987), pp. 475 - 480.

  12. Bounding laminations. Duke J. of Math. vol. 56 (1988), pp. 1 - 16.

  13. (with U. Oertel) Hyperbolic surface bundles over the circle. Progress in Knot theory and related topics. No. 56 (1997) pp. 121 - 142.

  14. Engulfing and subgroup separability for hyperbolic groups. Transactions of the American Math. Society. vol. 308 (1988), pp. 849 - 859.

  15. On the linear representation of braid groups. Transactions of the American Math. Society. vol. 311 (1989), pp. 535 - 560.

  16. On the linear representation of braid groups II. Duke J. of Math. vol. 59 (1989), pp. 443 - 460.

  17. On pseudo-Anosov maps which extend over two handlebodies. Proc. Edinburgh Math. Soc. vol. 33 (1990), pp.181 - 190.

  18. (with G. Niblo) Subgroup separability and 3-manifold groups. Math. Zeitschrift vol. 207 (1991), pp. 209 - 215.

  19. (with D. Cooper) An undetected slope in a knot manifold. Topology 90: Proceedings of the Ohio Conference. pp. 111- 121.

  20. (with C. Frohman) Casson's invariant and surgery on knots. Proc. Edinburgh Math. Soc. vol. 35 (1992), pp. 383 - 395.

  21. (with D. Cooper) Representing knot groups into SL(2,C). Proceedings American Math. Society vol. 116 (1992) pp. 547 - 549

  22. (with D. Cooper) Derivative varieties and the pure braid group. American J. of Math. vol. 115 (1993) pp. 137 - 160.

  23. (with A. W. Reid) Closed incompressible surfaces in 2-generator hyperbolic 3-manifolds with a single cusp. Proc. Edinburgh Math. Soc. vol. 36 (1993) pp. 501 - 513.

  24. (with M. Paton) The Burau Representation is not faithful for n >= 6. Topology vol. 32 (1993) pp. 439 - 447.

  25. (with D. Cooper) Roots of unity associated to the character variety of a knot complement. Journal of the Australian Math. Soc. vol. 55 (1993) pp. 90 - 99.

  26. (with J.S. Birman and J. Moody) Finite dimensional representations of Artin's Braid group. The Mathematical legacy of W. Magnus. Ed. W. Abikoff et al. Contemporary Math. vol. 169 pp. 123 -132.

  27. (with D. Cooper, M. Culler, H. Gillett and P. B. Shalen) Plane curves associated to character varieties of 3-manifolds. Inventiones Math. vol. 118 (1994) pp. 47 - 84.

  28. (with D. Cooper and A. W. Reid) Bundles and finite foliations. Inventiones Math. vol. 118 (1994) pp. 255 - 283.

  29. Constructing representations of braid groups. Communications in Geometry and Analysis. vol. 2 (1994) pp. 217 - 238.

  30. (with D. Cooper) A Kleinian group with contractible quotient not simply connected at infinity. Comment. Math. Helv. vol. 71 (1996) pp. 41 - 59.

  31. (with D. Cooper) Remarks on the A-polynomial of a knot. Journal of Knot Theory and its Ramifications. vol. 5, (1996) pp. 609 - 628.

  32. (with D. Cooper and A.W. Reid) Finite foliations and similarity interval exchange maps. Topology. vol 36, (1996) pp. 209 - 227.

  33. (with D. Cooper) The A-polynomial has ones in the corners. Bulletin London Math. Soc. vol.29 (1997), pp. 231--238.

  34. (with C. Maclachlan and A.W. Reid) Splitting groups of signature (1:n). Journal of Algebra. vol 185, (1996) pp. 329 - 341.

  35. (with D. Cooper) A presentation for the image of Burau(4) tensor Z2. Inventiones Math. vol. 127 (1997), pp. 535 - 570.

  36. (with D. Cooper) Foliations of some 3-manifolds which fiber over the circle. Proceedings American Math. Society vol. 126 (1998), pp. 925 - 931.

  37. (with D. Cooper) Representation theory and the A-polynomial of a knot. Chaos Theory \& Solitons, vol. 9 (1998) pp.749 - 765.

  38. (with D. Cooper and A. W. Reid) Essential surfaces in bounded 3-manifolds. Journal American Math. Society vol. 10 (1997) pp. 553 - 564.

  39. (with D. Cooper and A. W. Reid) Infinite Coxeter groups are virtually indicable. Proceedings Edinburgh Math. Soc. vol. 41 (1998) pp. 303 - 313.

  40. (with A.W. Reid) Simple quotients of hyperbolic 3-manifold groups. Proceedings American Math. Society vol. 126 (1998), pp. 877 - 880.

  41. (with A.W. Reid) Free products with amalgamation and p-adic Lie groups. Canadian Math. Bull. vol. 41 (1998), no. 4, pp. 423--433.

  42. (with A.W. Reid) On Fuchsian groups with the same set of axes. Bulletin London Math. Society vol. 30 (1998), no. 5, 533 - 538.

  43. (With D. Cooper) Trimming, J. of Experimental Mathematics, vol. 7 (1998) pp. 325 - 332.

  44. (With D. Cooper) The Burau representation modulo a small prime. Geometry and Topology Monographs, vol 1.The Epstein Birthday Schrift, pp. 127-138.

  45. (with D. Cooper) Free actions of finite groups on rational homology spheres. Topology and its Applications, vol. 101, (2000) pp. 143-148

  46. (with A. W. Reid) Commensurability and the character variety. Mathematical Research Letters, vol. 6 (1999) pp. 581- 592.

  47. (with D. Cooper) Virtually Haken Dehn filling. Journal of Differential Geometry, vol. 52, (1999) pp. 173-187.

  48. (with A. W. Reid) On the geometric boundaries of hyperbolic 4-manifolds. Geometry and Topology, vol. 4 (2000) pp. 171 - 178.

  49. (with D. Cooper) Some surface subgroups survive surgery. Geometry and Topology, vol. 5 (2001) pp. 347 - 367.

  50. (with I. Agol and A. W. Reid) The Bianchi groups are separable on geometrically finite subgroups. Annals of Math. vol. 153 (2001) pp. 599 - 621.

  51. (with A. W. Reid) On subgroup separability in hyperbolic Coxeter groups. Geom. Dedicata vol. 87 (2001) pp. 245 - 260.

  52. (with A. W. Reid) Integral points on character varieties. Math. Annalen vol. 325 (2003), pp. 299--321.

  53. (with A. W. Reid) The fundamental group of the double of the figure eight knot exterior is GFERF. Bulletin London Math. Society vol. 3 (2001) pp. 391 - 396.

  54. (with A. W. Reid) Constructing hyperbolic manifolds which bound geometrically. Math. Research Letters vol. 8 (2001), pp. 443--455

  55. (with A. W. Reid) Pseudomodular surfaces. J. Reine Angew. Math. vol. 552 (2002) pp. 77 - 100.

  56. (with A. W. Reid) All flat manifolds are cusps of hyperbolic orbifolds. Algebraic and Geometric Topology, vol. 2 (2002) pp. 285-296.

  57. (with C. McA. Gordon and A. W. Reid) Surface subgroups of Coxeter and Artin groups., Journal of Pure and Applied Algebra, vol.189 (2004) pp. 135 - 148

  58. (With A. W. Reid) On asymmetric hyperbolic manifolds., Math. Proc. Camb. Phil. Soc. vol.138 (2005) pp. 301 - 306

  59. (with A. W. Reid) Generalized Dedekind sums., Proceedings of the Casson Fest, Geometry and Topology Monographs, vol. 7 (2004), pp. 205--212.

  60. (with A. W. Reid) Surface subgroups and subgroup separability in 3-manifold topology, 25th Coloquio Brasileiro de Matematica, IMPA, Rio de Janeiro, 2005.

  61. (with T. Chinburg and A. W. Reid) Cusps of minimal noncompact arithmetic 3-orbifolds., Pure and Applied Math. Quarterly, vol. 4, (2008) pp. 1013--1031. (volume in honour of J. P. Serre)

  62. (with C. Maclachlan and A. W. Reid) Arithmetic fuchsian groups of genus zero., Pure and Applied Math. Quarterly vol. 2 (2006), pp. 569--599.

  63. (with A. W. Reid) Subgroup separability and virtual retractions of groups., Topology vol. 47 (2008) pp. 137 - 159. (Note that this article was submitted in 2004)

  64. (with D. Cooper and M. Thistlethwaite) Computing varieties of representations of hyperbolic 3-manifolds into $SL(4,{\bf R})$., J. of Experimental Math. vol. 15 (2006) pp. 291 -- 305.

  65. (with D. Cooper and M. Thistlethwaite) Flexing closed hyperbolic manifolds., Geometry & Topology vol. 11 (2007) pp. 2413-2440

  66. (with M. Lackenby and A. W. Reid) Covering spaces of arithmetic 3-orbifolds., Int. Math. Res. Not. IMRN (2008), no. 12, doi: rnn036 38 pages

  67. (with T. Chinburg, E. Hamilton and A. W. Reid) Geodesics and commensurability classes of arithmetic hyperbolic 3-manifolds., Duke Math. Journal vol. 145 (2008) pp 25-44.

  68. (with D. Cooper and A. W. Reid) On the virtual Betti numbers of arithmetic hyperbolic 3-manifolds. Geometry & Topology vol. 11 (2007) pp. 2265-2276

  69. (with A. Lubotzky and A. W. Reid) Heegaard genus and Property τ for hyperbolic 3-manifolds. Journal of Topology vol. 1 (2008) pp. 152 - 158.

  70. (with A. W. Reid) Finding fibre faces in finite covers. Math. Research Letters vol. 15 (2008) pp. 521-524

  71. (with M. Lackenby and A. W. Reid) LERF and the Lubotzky-Sarnak Conjecture Geometry and Topology, vol. 12 (2008) pp. 2047 - 2056

  72. (with D. Cooper and M. Thistlethwaite) Constructing non-congruence subgroups of flexible hyperbolic 3-manifold groups Proc. A.M.S. vol. 137 (2009), pp. 3943-3949

  73. (with A. W. Reid) Eigenvalues of hyperbolic elements in Kleinian groups. Contemporary Math. vol. 510, In the Tradition of Ahlfors-Bers, pp. 197-208

  74. (with C. Leininger and A. W. Reid) Commensurators of finitely generated non-free Kleinian groups. Algebraic and Geometric Topology, vol. 11 (2011) pp. 605-624

  75. (with A. W. Reid) Grothendieck's problem for 3-manifold groups. Groups, Geometry and Dynamics, vol. 5 (2011) pp. 479 - 499

  76. (with A. W. Reid) Small subgroups of SL(3,Z). Experimental Math. vol. 20, (2011) pp. 412-425.

  77. (with A. W. Reid and M. Thistlethwaite) Zariski dense surface subgroups in SL(3,Z). Geometry and Topology, vol. 15 (2011) pp. 1 - 9

  78. (with A. W. Reid) Fields of definition of canonical curves. Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory, Contemporary Math. vol. 541 (2011), pp. 247 - 257

  79. (with D. Cooper and S. Tillmann) On convex projective manifolds and cusps Advances in Math. vol. 277 (2015) pp. 181 - 251.

  80. (with A. W. Reid) Constructing thin subgroups in SL(4,R) International Math. Research Notices. vol. 2014 No. 7 (2014) pp. 2006 -- 2016. doi: 10.1093/imrn/rns281

  81. (with A. W. Reid) Constructing thin groups. Thin Groups and superstrong approximation, MSRI Publications vol. 61 (2013) pp. 151 -166.

  82. (with D. Cooper) A generalization of the Epstein-Penner construction to projective manifolds. Proc. A.M.S. vol. 143 (2015) pp. 4561-4569.

  83. (with M. Thistlethwaite) Lenstra-Hurwitz cliques and the class number one problem. Journal of Number Theory vol. 162 (2016) pp. 564 --- 577

  84. (with S. Ballas ) Constructing thin subgroups commensurable with the figure-eight knot group. Algebraic and Geometric Topology vol. 15 (2015), pp. 3009--3022. doi: 10.2140/agt.2015.15.3009

  85. (with A. W. Reid) Thin surface subgroups in cocompact lattices in SL(3,R) Illinois J. of Math. vol. 60 (2016) pp. 39 --- 53

  86. (with D. Cooper and S. Tillmann) Deforming convex projective manifolds Geometry and Topology, vol. 22 (2018), pp. 1349 -- 1404

  87. (with M. Thistlethwaite) Zariski dense surface subgroups in SL(4,Z). J. of Experimental Math. vol. 27 (2018) pp. 82 -- 92.

  88. (with M. Thistlethwaite) The Dimension of the Hitchin Component for Triangle Groups. Geometriae Dedicata vol. 200 (2019) pp. 363 -- 370. https://doi.org/10.1007/s1071

  89. (with A. W. Reid) Sequences of high rank lattices of large systole containing a fixed genus surface group. New York Journal of Math, vol. 25 (2019), pp. 145 -- 155.

  90. (with S. Ballas) Constructing thin subgroups of SL(n+1,R) via bending. Algebraic and Geometric Topology, vol. 20 (2020), pp. 2071 -- 2093.

  91. (with A. Kontorovich, A. Lubotzky & A. W. Reid) What is.... a Thin Group? Notices A.M.S. vol. 66 (2019) pp. 905 -- 910.

  92. (with A. W. Reid) Virtually spinning hyperbolic manifolds. Proceedings of the Edinburgh Math. Soc. vol. 63 (2020), pp. 305 -- 313.

  93. (with M. Thistlethwaite) Zariski dense surface groups in SL(2k+1,Z). Geometry and Topology, vol. 28 (2024) pp. 1153 -- 1166

  94. (with A. W. Reid) Strongly dense representations of surface groups. To appear Edinburgh Journal of Math.

  95. (with A. W. Reid & M. Wolff ) Most Hitchin representations are strongly dense. To appear in Michigan Journal of Math.
A preprint accessible above may differ somewhat from its final published version. Preprints are in .pdf format and so may be read using the free Acrobat Reader.