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Foliations of codimension 2 with all leaves compact on closed 3-, 4-, and 5-manifolds. (English) Zbl 0369.57008


MSC:

57R30 Foliations in differential topology; geometric theory
57M05 Fundamental group, presentations, free differential calculus
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References:

[1] Barden, D.: Simply connected 5-manifolds. Ann. of Math., II. Ser.82, 365-385 (1965) · Zbl 0136.20602 · doi:10.2307/1970702
[2] Bing, R.H.: The Cartesian product of a certain non-manifold and a line isE 4. Ann. of Math., II. Ser.70, 399-412 (1959) · Zbl 0089.39501 · doi:10.2307/1970322
[3] Birman, J.S., Hilden, H.M.: Lifting and projecting homeomorphisms. Arch. der Math.23, 428-434 (1972) · Zbl 0247.55001 · doi:10.1007/BF01304911
[4] Edwards, R., Millett, K., Sullivan, D.: Foliations with all leaves compact. Topology16, 13-32 (1977) · Zbl 0356.57022 · doi:10.1016/0040-9383(77)90028-3
[5] Epstein, D.B.A.: Curves on 2-manifolds and isotopies. Acta math.115, 83-107 (1966) · Zbl 0136.44605 · doi:10.1007/BF02392203
[6] Epstein, D.B.A.: Periodic flows on 3-manifolds. Ann. of Math., II. Ser.95, 66-82 (1972) · Zbl 0231.58009 · doi:10.2307/1970854
[7] Fox, R.H.: On a problem of S. Ulam concerning Cartesian products. Fundamenta Math.34, 278-287 (1949) · Zbl 0033.02403
[8] Greenberg, L.: On discrete groups of motions. Canadian J. Math.12, 415-426 (1960) · Zbl 0096.02102 · doi:10.4153/CJM-1960-036-8
[9] Hamstrom, M.-E.: The space of homeomorphisms on a torus. Illinois J. Math.9, 59-65 (1965) · Zbl 0127.13505
[10] Hamstrom, M.-E.: Homotopy properties of the space of homeomorphisms onP 2 and the Klein bottle. Trans. Amer. math. Soc.120, 37-45 (1965) · Zbl 0148.17201
[11] Hamstrom, M.-E.: Homotopy groups of the space of homeomorphisms on a 2-manifold. Illinois J. Math.10, 563-573 (1969) · Zbl 0151.33002
[12] Heil, W.: On IP2-irreducible 3-manifolds. Bull. Amer. math. Soc.75, 772-775 (1969) · Zbl 0176.21401 · doi:10.1090/S0002-9904-1969-12283-4
[13] Hempel, J., Jaco, W.: Fundamental groups of 3-manifolds which are extensions. Ann. of Math., II. Ser.95, 86-98 (1972) · Zbl 0226.57003 · doi:10.2307/1970856
[14] Holmann, H.: Seifertsche Faserräume. Math. Ann.157, 138-166 (1964) · Zbl 0123.16501 · doi:10.1007/BF01362671
[15] Laudenbach, F.: Topologie de dimension trois. Homotopie et isotopie. Asterisque12, 1-152 (1974) · Zbl 0293.57004
[16] Macbeath, A.M.: Geometric realizations of isomorphisms between plane groups. Bull. Amer. math. Soc.71, 629-630 (1965) · Zbl 0137.40102 · doi:10.1090/S0002-9904-1965-11368-4
[17] Macbeath, A.M.: The classification of non-euclidean plane cristallographic groups. Canadian J. Math.19, 1192-1205 (1967) · Zbl 0183.03402 · doi:10.4153/CJM-1967-108-5
[18] Nielsen, J.: Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. Acta math.50, 189-358 (1927) · JFM 53.0545.12 · doi:10.1007/BF02421324
[19] Orlik, P., Vogt, E., Zieschang, H.: Zur Topologie dreidimensionaler gefaserter Mannigfaltigkeiten. Topology6, 49-64 (1967) · Zbl 0147.23503 · doi:10.1016/0040-9383(67)90013-4
[20] Peczynski, N., Rosenberger, G., Zieschang, H.: Über Erzeugende ebener diskontinuierlicher Gruppen. Inventiones math.29, 161-180 (1975) · Zbl 0311.20031 · doi:10.1007/BF01390193
[21] Vogt, E.: Seifertsche Faserräume. Diplomarbeit, Frankfurt 1968
[22] Vogt, E.: Stable foliations of 4-manifolds by closed surfaces I. Inventiones math.22, 321-348 (1973) · Zbl 0268.57012 · doi:10.1007/BF01389675
[23] Vogt, E.: Foliations of codimension 2 with all leaves compact. Manuscripta math.18, 187-212 (1976) · Zbl 0316.57014 · doi:10.1007/BF01184305
[24] Vogt, E.: Projecting Isotopies of sufficiently largeP 2-irreducible 3-Manifolds. To appear in Arch. der Math. · Zbl 0404.57012
[25] Waldhausen, F.: Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I,II. Inventiones math.3, 308-333, and4, 87-117 (1967) · Zbl 0168.44503 · doi:10.1007/BF01402956
[26] Waldhausen, F.: Gruppen mit Zentrum und dreidimensionale Mannigfaltigkeiten. Topology6, 505-517 (1967) · Zbl 0172.48704 · doi:10.1016/0040-9383(67)90008-0
[27] Waldhausen, F.: On irreducible 3-manifolds which are sufficiently large. Ann. of Math. II. Ser.87, 56-88 (1968) · Zbl 0157.30603 · doi:10.2307/1970594
[28] Whitehead, J.H.C.: On the homotopy type of manifolds. Ann. of Math., II. Ser.41, 825-832 (1940) · Zbl 0025.09304 · doi:10.2307/1968862
[29] Zieschang, H.: Über Automorphismen ebener diskontinuierlicher Gruppen. Math. Ann.166, 148-167 (1966) · Zbl 0151.33102 · doi:10.1007/BF01361444
[30] Zieschang, H.: On Toric Fiberings over Surfaces. Math. Notes5, 569-576 (1969) · Zbl 0186.57504
[31] Zieschang, H.: On extensions of fundamental groups of surfaces and related groups. Bull. Amer. math. Soc.77, 1116-1119 (1971) · Zbl 0219.55001 · doi:10.1090/S0002-9904-1971-12887-2
[32] Zieschang, H.: On the homeotopy groups of surfaces. Math. Ann.206, 1-21 (1973) · Zbl 0256.55001 · doi:10.1007/BF01431525
[33] Zieschang, H., Vogt, E., Coldewey, H.-D.: Flächen und ebene diskontinuierliche Gruppen. Lecture Notes in Math. 122, Berlin-Heidelberg-New York: Springer 1970 · Zbl 0204.24002
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