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Cantwell, John; Conlon, Lawrence

Nonexponential leaves at finite level. (English) Zbl 0487.57009

Trans. Am. Math. Soc. 269, 637-661 (1982).
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scan of Zbl 0487.57009

Cited in 2 Reviews
Cited in 7 Documents

MSC:

57R30 Foliations in differential topology; geometric theory

Keywords:

level of a leaf; ends of leaves; growth type of leaves; codimension-one foliation on a closed 3-manifold; local minimal set of locally dense type; transversely analytic codimension-one foliation

Citations:

Zbl 0484.57015
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Full Text: DOI

References:

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[2] Lawrence Conlon, Transversally parallelizable foliations of codimension two, Trans. Amer. Math. Soc. 194 (1974), 79 – 102, erratum, ibid. 207 (1975), 406. · Zbl 0288.57011
[3] John Cantwell and Lawrence Conlon, Leaf prescriptions for closed 3-manifolds, Trans. Amer. Math. Soc. 236 (1978), 239 – 261. , https://doi.org/10.1090/S0002-9947-1978-0645738-9 John Cantwell and Lawrence Conlon, Leaves with isolated ends in foliated 3-manifolds, Topology 16 (1977), no. 4, 311 – 322. · Zbl 0385.57007 · doi:10.1016/0040-9383(77)90038-6
[4] John Cantwell and Lawrence Conlon, Leaf prescriptions for closed 3-manifolds, Trans. Amer. Math. Soc. 236 (1978), 239 – 261. , https://doi.org/10.1090/S0002-9947-1978-0645738-9 John Cantwell and Lawrence Conlon, Leaves with isolated ends in foliated 3-manifolds, Topology 16 (1977), no. 4, 311 – 322. · Zbl 0385.57007 · doi:10.1016/0040-9383(77)90038-6
[5] John Cantwell and Lawrence Conlon, Growth of leaves, Comment. Math. Helv. 53 (1978), no. 1, 93 – 111. · Zbl 0368.57009 · doi:10.1007/BF02566067
[6] John Cantwell and Lawrence Conlon, Poincaré-Bendixson theory for leaves of codimension one, Trans. Amer. Math. Soc. 265 (1981), no. 1, 181 – 209. · Zbl 0484.57015
[7] John Cantwell and Lawrence Conlon, Smoothing fractional growth, Tôhoku Math. J. (2) 33 (1981), no. 2, 249 – 262. · Zbl 0477.57014 · doi:10.2748/tmj/1178229452
[8] Paul R. Dippolito, Codimension one foliations of closed manifolds, Ann. of Math. (2) 107 (1978), no. 3, 403 – 453. · Zbl 0418.57012 · doi:10.2307/1971123
[9] Hans Freudenthal, Über die Enden topologischer Räume und Gruppen, Math. Z. 33 (1931), no. 1, 692 – 713 (German). · Zbl 0002.05603 · doi:10.1007/BF01174375
[10] Sue E. Goodman, Closed leaves in foliations of codimension one, Comment. Math. Helv. 50 (1975), no. 3, 383 – 388. · Zbl 0318.57027 · doi:10.1007/BF02565757
[11] Gilbert Hector, Leaves whose growth is neither exponential nor polynomial, Topology 16 (1977), no. 4, 451 – 459. · Zbl 0379.57005 · doi:10.1016/0040-9383(77)90050-7
[12] Gilbert Hector, Croissance des feuilletages presque sans holonomie, Differential topology, foliations and Gelfand-Fuks cohomology (Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, 1976) Lecture Notes in Math., vol. 652, Springer, Berlin, 1978, pp. 141 – 182 (French). · Zbl 0393.57005
[13] Heinz Hopf, Enden offener Räume und unendliche diskontinuierliche Gruppen, Comment. Math. Helv. 16 (1944), 81 – 100 (German). · Zbl 0060.40008 · doi:10.1007/BF02568567
[14] Claude Lamoureux, Sur quelques phénomènes de captage, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 4, 229 – 243 (French, with English summary). · Zbl 0251.57009
[15] J. F. Plante, Foliations with measure preserving holonomy, Ann. of Math. (2) 102 (1975), no. 2, 327 – 361. · Zbl 0314.57018 · doi:10.2307/1971034
[16] L. S. Pontryagin, Topological groups, Translated from the second Russian edition by Arlen Brown, Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966. · Zbl 0022.17104
[17] Walter Rudin, Principles of mathematical analysis, 3rd ed., McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976. International Series in Pure and Applied Mathematics. · Zbl 0346.26002
[18] Richard Sacksteder, Foliations and pseudogroups, Amer. J. Math. 87 (1965), 79 – 102. · Zbl 0136.20903 · doi:10.2307/2373226
[19] Paul A. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliations, Ann. of Math. (2) 100 (1974), 386 – 400. · Zbl 0295.57010 · doi:10.2307/1971077
[20] William P. Thurston, A local construction of foliations for three-manifolds, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 315 – 319.
[21] D. Tischler, On fibering certain foliated manifolds over \?\textonesuperior , Topology 9 (1970), 153 – 154. · Zbl 0177.52103 · doi:10.1016/0040-9383(70)90037-6
[22] Nobuo Tsuchiya, Leaves with nonexact polynomial growth, Tôhoku Math. J. (2) 32 (1980), no. 1, 71 – 77. · Zbl 0448.57010 · doi:10.2748/tmj/1178229683
[23] Nobuo Tsuchiya, Growth and depth of leaves, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979), no. 3, 473 – 500. · Zbl 0448.57009
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