Duke Mathematical Journal

Dynamical systems and the homology norm of a $3$-manifold, I: efficient intersection of surfaces and flows

Lee Mosher

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Article information

Duke Math. J. Volume 65, Number 3 (1992), 449-500.

First available in Project Euclid: 20 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 58F15


Mosher, Lee. Dynamical systems and the homology norm of a 3 -manifold, I: efficient intersection of surfaces and flows. Duke Math. J. 65 (1992), no. 3, 449--500. doi:10.1215/S0012-7094-92-06518-5. http://projecteuclid.org/euclid.dmj/1077295267.

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  • [BW] J. Birman and R. Williams, Knotted periodic orbits in dynamical system. II. Knot holders for fibered knots, Low-dimensional topology (San Francisco, Calif., 1981) ed. S. Lomonaco, Contemp. Math., vol. 20, Amer. Math. Soc., Providence, RI, 1983, pp. 1–60.
  • [Bon] F. Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. (2) 124 (1986), no. 1, 71–158.
  • [Bow] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460.
  • [CE] C. Conley and R. Easton, Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc. 158 (1971), 35–61.
  • [CM] J. Christy and L. Mosher, Pseudo-Anosov flows and dynamic pairs of branched surfaces, in preparation.
  • [CT] J. Cannon and W. P. Thurston, Group invariant Peano curves, preprint.
  • [FLP] A. Fathi, F. Laudenbach, and V. Poenaru, Travaux de Thurston sur les surfaces, Astérisque, vol. 66-67, Société Mathématique de France, Paris, 1979.
  • [FO] W. Floyd and U. Oertel, Incompressible surfaces via branched surfaces, Topology 23 (1984), no. 1, 117–125.
  • [Fr1] D. Fried, The geometry of cross sections to flows, Topology 21 (1982), no. 4, 353–371.
  • [Fr2] D. Fried, Fibrations over $S^1$ with pseudo-Anosov monodromy, Astérisque 66-67 (1979), 251–266, exposé 14 of Travaux de Thurston sur les Surfaces.
  • [G] M. Gabai, Essential laminations transverse to finite depth foliations, in preparation.
  • [GO] D. Gabai and U. Oertel, Essential laminations in $3$-manifolds, Ann. of Math. (2) 130 (1989), no. 1, 41–73.
  • [Gr] M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263.
  • [HPS] M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds, Springer-Verlag, Berlin, 1977.
  • [L] G. Levitt, Foliations and laminations on hyperbolic surfaces, Topology 22 (1983), no. 2, 119–135.
  • [Mor] J. Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, The Smith conjecture (New York, 1979) eds. J. Morganand and H. Bass, Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 37–125.
  • [Mos1] L. Mosher, Examples of quasi-geodesic flows on hyperbolic $3$-manifolds, to appear in Proceedings of the Ohio State University Research Semester in Low-Dimensional Topology.
  • [Mos2] L. Mosher, Dynamical systems and the homology norm of a $3$-manifold, II, to appear in Invent. Math.
  • [Mu] J. Munkres, Topology: a first course, Prentice-Hall Inc., Englewood Cliffs, N.J., 1975.
  • [O] U. Oertel, Incompressible branched surfaces, Invent. Math. 76 (1984), no. 3, 385–410.
  • [P] R. Penner, Combinatorics of train tracks, to appear.
  • [Ra] M. Ratner, Markov splitting for an U-flow in three-dimensional manifold, Math. Notes 9 (1969), 880–886, translated from Mat. Zemetki 9 (1969) 693–704.
  • [Ro] R. Roussarie, Plongements dans les variétés feuilletées et classification de feuilletages sans holonomie, Inst. Hautes Études Sci. Publ. Math. (1974), no. 43, 101–141.
  • [Sm] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.
  • [T1] W. P. Thurston, A norm for the homology of $3$-manifolds, Mem. Amer. Math. Soc. 59 (1986), no. 339, i–vi and 99–130.
  • [T2] W. P. Thurston, The Geometry and Topology of $3$-manifolds, 1978, chapter 8 and 9 of lecture notes based on his course at Princeton Univ.

See also

  • See also: Lee Mosher. Dynamical systems and the homology norm of a 3-manifold. II. Invent. Math. Vol. 107 (1992), pp. 243–281.