John Ratcliffe

Publications

Research Articles

  1. John G. Ratcliffe, Crossed extensions, Trans. Amer. Math. Soc. 257 (1980), 73-89.
  2. John G. Ratcliffe, On the second transgression of the Lyndon-Hochschild- Serre spectral sequence, J. Algebra 61 (1979), 593-598.
  3. John G. Ratcliffe, Free and projective crossed modules, J. London Math. Soc.22 (1980), 66-74.
  4. Philip S. Hirschhorn and John G. Ratcliffe, A simple proof of the algebraic unknotting of spheres in codimension two, Amer. J. of Math.102 (1980), 489-491.
  5. Mauricio A. Gutierrez and John G. Ratcliffe, On the second homotopy group, Quart. J. Math. Oxford 32 (1981), 45-55.
  6. John G. Ratcliffe, On the ends of higher dimensional knot groups, J. Pure Appl. Algebra 20 (1981), 317-324.
  7. John G. Ratcliffe, On one-relator groups which satisfy Poincare duality, Math. Z. 177 (1981), 425-438.
  8. A. M. Brunner and J. G. Ratcliffe, Finite 2-complexes with infinitely generated groups of self homotopy equivalences, Proc. Amer. Math. Soc. 86 (1982), 525-530.
  9. John G. Ratcliffe, Finiteness conditions for groups, J. Pure Appl. Algebra 27 (1983), 173-185.
  10. John G. Ratcliffe, A fibered knot in a homology 3-sphere whose group is nonclassical, In: Low Dimensional Topology, Contemp. Math. 20 (1983), 327-339.
  11. John G. Ratcliffe, Lyndon’s contribution to cohomology of groups, In: Contributions to Group Theory, Contemp. Math. 33 (1984), 24-28. 5
  12. John G. Ratcliffe, The cohomology ring of a one-relator group, In: Contributions to Group Theory, Contemp. Math. 33 (1984), 455-466.
  13. Nathan Habegger, Vaughan Jones, Pino Ortiz and John Ratcliffe, Relative cohomology of groups, Comment. Math. Helv. 59 (1984), 149-164.
  14. John G. Ratcliffe, On complexes dominated by a two-complex, In: Combinatorial Group Theory and Topology, Ann. Math. Studies 111 (1986), 221-254.
  15. John G. Ratcliffe, Euler characteristics of 3-manifold groups and discrete subgroups of SL(2,C), J. Pure Appl. Algebra. 44 (1987), 303- 314.
  16. John G. Ratcliffe, On the uniqueness of amalgamated product decompositions of a group. In: Combinatorial Group Theory, Contemp. Math. 109 (1990), 139-146.
  17. Magnhild Lien and John G. Ratcliffe, On the uniqueness of HNN decompositions of a group J. Pure Appl. Algebra. 75 (1991), 51-62.
  18. John G. Ratcliffe, On the isometry groups of hyperbolic manifolds, In: The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry and Special Functions, Contemp. Math. 169 (1994), 491-495.
  19. John G. Ratcliffe and Steven T. Tschantz, Volumes of integral congruence hyperbolic manifolds, J. Reine Angew. Math. 488 (1997), 55-78.
  20. John G. Ratcliffe and Steven T. Tschantz, On the representation of integers by the Lorentzian quadratic form, J. Funct. Anal. 150 (1997), 498-525.
  21. John G. Ratcliffe and Steven T. Tschantz, Gravitational instantons of constant curvature, Classical and Quantum Gravity, 15 (1998), 2613- 2627.
  22. John G. Ratcliffe and Steven T. Tschantz, On the torsion of the group O(n, 1;Z) of integral Lorentzian (n+1)x(n+1) matrices, J. Pure and Appl. Algebra. 136 (1999), 157-181.
  23. John G. Ratcliffe, On the isometry groups of hyperbolic orbifolds, Geometriae Dedicata 78 (1999), 63-67.
  24. N.W. Johnson, R. Kellerhals, J.G. Ratcliffe, and S.T. Tschantz, The size of a hyperbolic Coxeter simplex, Transformation Groups 4 (1999), 329-353.
  25. John G. Ratcliffe and Steven T. Tschantz, Spin and complex structures on flat gravitational instantons, Classical and Quantum Gravity 17 (2000), 179-188.
  26. John G. Ratcliffe and Steven T. Tschantz, The volume spectrum of hyperbolic 4-manifolds, Experimental Math. 9 (2000), 101-125.
  27. John G. Ratcliffe and Steven T. Tschantz, On the growth of the number of hyperbolic gravitational instantons with respect to volume, Classical and Quantum Gravity 17 (2000), 2999-3007.
  28. John G. Ratcliffe and Steven T. Tschantz, On the Davis hyperbolic 4-manifold, Topology Appl. 111 (2001), 327-342.
  29. N.W. Johnson, R. Kellerhals, J.G. Ratcliffe, and S.T. Tschantz, Commensurability classes of hyperbolic Coxeter groups, Linear Algebra Appl. 345 (2002), 119-147.
  30. John G. Ratcliffe, Hyperbolic Manifolds, Chapter in: Handbook of Geometric Topology, Edited by R.J.Daverman and R.B.Sher, Elsevier Sciences B.V., Amsterdam, (2002), 899-920.
  31. John G. Ratcliffe and Steven T. Tschantz, Integral congruence two hyperbolic 5-manifolds, Geometriae Dedicata 107 (2004), 187-209.
  32. M. Anderson, S. Carlip, J. G. Ratcliffe, S. Surya, S. T. Tschantz, Peaks in the Hartle-Hawking wave function from sums over topologies, Class. and Quantum Grav. 21 (2004), 729-741.
  33. John G. Ratcliffe and Steven T. Tschantz, Some examples of aspherical 4-manifolds that are homology 4-spheres, Topology 44 (2005), 341-350.
  34. Brent Everitt, John G. Ratcliffe, and Steven T. Tschantz, The smallest hyperbolic 6-manifolds, Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 40-46.
  35. Dubravko Ivansic, John G. Ratcliffe, and Steven T. Tschantz, Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure, Algebraic & Geometric Topology 5 (2005), 999-1026.
  36. John G. Ratcliffe, The geometry of hyperbolic manifolds of dimension at least four, In: Non-Euclidean Geometries, Edited by A. Prekopa and E. Molnar, Math. Appl., 581 (2006), Springer, New York, 269-286.
  37. Michael L. Mihalik, John G. Ratcliffe, and Steven T. Tschantz, Matching theorems for systems of a finitely generated Coxeter group, Algebr. Geom. Topol. 7 (2007), 919-956.
  38. John G. Ratcliffe, and Steven T. Tschantz, Chordal Coxeter groups, Geom. Dedicata 136 (2008), 57-77.
  39. Michael Mihalik, John Ratcliffe, and Steven Tschantz, Quotient isomorphism invariants of a finitely generated Coxeter group, In: Aspects of Infinite Groups, Edited by B. Fine, G. Rosenberger, and D. Spellman, Algebra Discrete Math. 1 (2008), 212-227, World Sci. Publ., Hackensack, NJ.
  40. John G. Ratcliffe and Steven T. Tschantz, Abelianization of space groups, Acta Crystallogr. A65 (2009), 18-27.
  41. Michael L. Mihalik and John G. Ratcliffe, On the rank of a Coxeter group, J. Group Theory, 12 (2009), 449-464.
  42. John G. Ratcliffe, and Steven T. Tschantz, Fibered orbifolds and crystallographic groups,
    Algebr. Geom. Topol. 10 (2010), 1627-1664.
  43. Brent Everitt, John G. Ratcliffe, and Steven T. Tschantz, Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel, Math. Ann. 354 (2012), 871-905.
  44. John G. Ratcliffe, and Steven T. Tschantz, On volumes of hyperbolic Coxeter polytopes and quadratic forms, Geom. Dedicata 163 (2013), 285-299.
  45. John G. Ratcliffe, and Steven T. Tschantz, JSJ decompositions of Coxeter groups over FA subgroups, Topology Proc. 42 (2013), 57-72.
  46. John G. Ratcliffe, On normal subgroups of an amalgamated product of groups
    with applications to knot theory, Bol. Soc. Mat. Mex., 20 (2014), 287-296.
  47. John G. Ratcliffe, and Steven T. Tschantz, The Calabi construction for compact flat orbifolds
    Topology Appl., 178 (2014), 87-106.
  48. John G. Ratcliffe, and Steven T. Tschantz, On the isometry group of a compact flat orbifold,
    Geom. Dedicata, 177 (2015), 43-60.

Books

  1. Contributions to Group Theory, edited by Kenneth I. Appel, John G. Ratcliffe and Paul E. Schupp, American Mathematical Society, Providence (1984), 519 pages.
  2. Philip Crooke and John Ratcliffe, A Guidebook to Calculus with Mathematica, Wadsworth Publishing Company, Belmont, California (1991), 256 pages.
  3. John G. Ratcliffe, Foundations of Hyperbolic Manifolds, Graduate Texts in Math. 149, Springer-Verlag, New York, (1994), 747 pages.
  4. John G. Ratcliffe, Foundations of Hyperbolic Manifolds, Second Edition, Graduate Texts in Math. 149, Springer-Verlag, New York, (2006), 779 pages.

Book Reviews

  1. Functions on Manifolds, V.V. Sharko, Math. Reviews, (1994), Review 94j:57001.
  2. Two-dimensional Homotopy and Combinatorial Group Theory, C. Hog- Angeloni, W. Metzler, and A.J. Sieradski, Math. Reviews, (1995), Review 95g:57006.
  3. Introduction to Hyperbolic Geometry, A. Ramsay and R.D. Richtmyer, Amer. Math. Monthly, 103 (1996), 203-204.
  4. Stable modules and the D(2)-problem, F.E.A. Johnson, Math. Reviews, (2005), Review 2005b:57008.
  5. Topological Methods in Group Theory, R. Geoghegan, Math. Reviews, (2008), Review 2008j:57002.

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Contact Information

John G. Ratcliffe
Professor of Mathematics
Office: Stevenson Center 1508
Department of Mathematics
1326 Stevenson Center
Nashville, TN 37240
(615) 322-6665
Email