Homology Hopf surfaces

Wolfgang Ebeling; Christian Okonek

Compositio Mathematica (1994)

  • Volume: 91, Issue: 3, page 277-304
  • ISSN: 0010-437X

How to cite

top

Ebeling, Wolfgang, and Okonek, Christian. "Homology Hopf surfaces." Compositio Mathematica 91.3 (1994): 277-304. <http://eudml.org/doc/90292>.

@article{Ebeling1994,
author = {Ebeling, Wolfgang, Okonek, Christian},
journal = {Compositio Mathematica},
keywords = {product of the circle with a Seifert 3-manifold; rational homology 3- sphere; homology Hopf surface; complex surface; rational homology groups; diffeomorphic; Seifert 3-manifold; complex structures},
language = {eng},
number = {3},
pages = {277-304},
publisher = {Kluwer Academic Publishers},
title = {Homology Hopf surfaces},
url = {http://eudml.org/doc/90292},
volume = {91},
year = {1994},
}

TY - JOUR
AU - Ebeling, Wolfgang
AU - Okonek, Christian
TI - Homology Hopf surfaces
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 91
IS - 3
SP - 277
EP - 304
LA - eng
KW - product of the circle with a Seifert 3-manifold; rational homology 3- sphere; homology Hopf surface; complex surface; rational homology groups; diffeomorphic; Seifert 3-manifold; complex structures
UR - http://eudml.org/doc/90292
ER -

References

top
  1. [BPV] Barth, W., Peters, C., Van de Ven, A.: Compact Complex Surfaces. Springer, Berlin, Heidelberg, New York, Tokyo, 1984. Zbl0718.14023MR749574
  2. [Bo1] Bogomolov, F.: Classification of surfaces of class VII with b2 = 0. Math. USSR Izv.10 (1976) 255-269. Zbl0352.32020
  3. [Bo2] Bogomolov, F.: Surfaces of class VII0 and affine geometry. Math. USSR Izv.21 (1983), 31-73. Zbl0527.14029
  4. [BH] Braam, P., Hurtubise, J.: Instantons on Hopf surfaces and monopoles on solid tori. J. reine angew. Math.400 (1989) 146-172. Zbl0669.32012MR1013728
  5. [BV] Brieskorn, E., Van de Ven, A.: Some complex structures on products of homotopy spheres. Topology7 (1968), 389-393. Zbl0174.54901MR233360
  6. [CR1] Conner, P.E., Raymond, F.: Holomorphic Seifert fiberings. In: Proc. Second Conference on Compact Transformation Groups, Part II (Lecture Notes in Math., vol. 299) Springer, Berlin, Heidelberg, New York, 1972, pp. 124-204. Zbl0266.57009MR590802
  7. [CR2] Conner, P.E., Raymond, F.: Deforming homotopy equivalences to homeomorphisms in aspherical manifolds. Bull. Amer. Math. Soc.83 (1977), 36-85. Zbl0341.57003MR467777
  8. [Fl] Floer, A.: An instanton invariant for 3-manifolds. Commun. Math. Phys.118 (1988) 215-240. Zbl0684.53027MR956166
  9. [FM] Friedman, R., Morgan, J.W.: Algebraic surfaces and 4-manifolds: some conjectures and speculations. Bull. Amer. Math. Soc. (N.S.) 18 (1988) 1-19. Zbl0662.57016MR919651
  10. [GS] Gurjar, R.V., Shastri, A.R.: Covering spaces of an elliptic surface. Comp. Math.54 (1985) 95-104. Zbl0583.14013MR782388
  11. [Hol] Holmann, H.: Seifertsche Faserräume. Math. Ann.157 (1964) 138-166. Zbl0123.16501MR170349
  12. [Hop] Hopf, H.: Zur Topologie der komplexen Mannigfaltigkeiten. In: Studies and Essays presented to R. Courant, Interscience, New York, 1948, pp. 167-185. Zbl0033.02501MR23054
  13. [Ii] Iitaka, S.: Deformations of compact complex surfaces. I: In: Global Analysis. Papers in Honor of K. Kodaira. (D. C. Spencer, S. Iyanaga, eds.) Univ. Tokyo Press, Tokyo1969, pp. 267-272.II: J. Math. Soc. Japan22 (1970) 247-261.III: ibid.23 (1971) 692-705. Zbl0219.32012MR254879
  14. [In1] Inoue, M.: On surfaces of class VII0. Invent. Math.24 (1974) 269-310. Zbl0283.32019MR342734
  15. [In2] Inoue, M.: An example of an analytic surface. Sugaku27 (1975), 358-364 (Japanese). MR590800
  16. [Ka] Kato, M.: Topology of Hopf surfaces. J. Math. Soc. Japan27 (1975) 222-238. Zbl0301.32025MR402128
  17. [Ko1] Kodaira, K.: On the structure of compact complex analytic surfaces. I: Amer. J. Math.86 (1964) 751-798.II: ibid.88 (1966) 682-721.III: ibid.90 (1968) 55-83.IV: ibid.90 (1968) 1048-1066. Zbl0193.37702MR187255
  18. [Ko2] Kodaira, K.: Complex structures on S1 x S3. Proc. Nat. Acad. Sci. U.S.A.55 (1966) 240-243. Zbl0141.27402MR196769
  19. [LYZ] Li, J., Yau, S.T., Zheng, F.: A simple proof of Bogomolov's theorem on class VII0 surfaces with b2 = 0. Illinois J. of Math.34 (1990) 217-220. Zbl0705.32018MR1046563
  20. [M] Mandelbaum, R.: Four-dimensional topology: an introduction. Bull. Amer. Math. Soc.(N.S.) 2 (1980) 1-159. Zbl0476.57005MR551752
  21. [Na] Nakamura, I.: VII0 surfaces and a duality of cusp singularities. In: Classification of Algebraic and Analytic Manifolds (K. Ueno, ed.) (Prog. Math.39) Birkhäuser, Boston, 1983, pp. 333-378. Zbl0557.32005MR728613
  22. [Ne1] Neumann, W.D.: S1-Actions and the α-Invariant of their Involutions. Bonner Math. Schriften44, Bonn, 1970. Zbl0219.57030
  23. [Ne2] Neumann, W.D.: Geometry of quasihomogeneous surface singularities. Proc. Symp. Pure Math.40 (1983), Part 2, 245-258. Zbl0519.32011MR713253
  24. [NR] Neumann, W.D., Raymond, F.: Seifert manifolds, plumbing, μ-invariant and orientation reversing maps. In: Algebraic and Geometric Topology (K. C. Millet, ed.). Proc. Santa Barbara 1977 (Lect. Notes in Math., vol. 664) Springer, Berlin, Heidelberg, New York, 1978, pp. 162-196. Zbl0401.57018
  25. [O] Orlik, P.: Seifert Manifolds. (Lect. Notes in Math., vol. 291) Springer, Berlin, Heidelberg, New York, 1972. Zbl0263.57001MR426001
  26. [OVZ] Orlik, P., Vogt, E., Zeischang, H.: Zur Topologie gefaserter dreidimensionaler Mannigfaltigkeiten. Topology6 (1967), 49-64. Zbl0147.23503MR212831
  27. [P] Pinkham, H.: Normal surface singularities with C* action. Math. Ann.227 (1977) 183-193. Zbl0331.14018MR432636
  28. [S1] Scott, P.: There are no fake Seifert fibre spaces with infinite π1. Annals of Math.117 (1983), 35-70. Zbl0516.57006
  29. [S2] Scott, P.: The geometries of 3-manifolds. Bull. London Math. Soc.15 (1983) 401-487. Zbl0561.57001MR705527
  30. [W1] Waldhausen, F.: Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I: Invent. Math.3 (1967) 308-333.II: Invent. Math.4 (1967) 87-117. Zbl0168.44503MR235576
  31. [W2] Waldhausen, F.: On irreducible 3-manifolds which are sufficiently large. Ann. of Math.87 (1968) 56-88. Zbl0157.30603MR224099
  32. [W3] Wall, C.T.C.: Geometric structures on compact complex analytic surfaces. Topology25 (1986) 119-153. Zbl0602.57014MR837617
  33. [Z] Zieschang, H.: On toric fiberings over surfaces. Mat. Zametki5:5 (1969) 569-576(Engl. Translation in: Math. Notes Acad. Sc. USSR5:5 (1969) 341-345). Zbl0186.57504MR248835

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.