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., To appear Pure and Applied Math. Quarterly, 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., To appear International Math. Research Notices

  67. (with T. Chinburg, E. Hamilton and A. W. Reid) Geodesics and commensurability classes of arithmetic hyperbolic 3-manifolds., To appear in Duke Math. J.

  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 To appear in Geometry and Topology.
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.