Holomorphic submersions from Stein manifolds
- [1] Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia)
Annales de l’institut Fourier (2004)
- Volume: 54, Issue: 6, page 1913-1942
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topForstnerič, Franc. "Holomorphic submersions from Stein manifolds." Annales de l’institut Fourier 54.6 (2004): 1913-1942. <http://eudml.org/doc/116164>.
@article{Forstnerič2004,
abstract = {We establish the homotopy classification of holomorphic submersions from Stein manifolds
to Complex manifolds satisfying an analytic property introduced in the paper. The result
is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.},
affiliation = {Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia)},
author = {Forstnerič, Franc},
journal = {Annales de l’institut Fourier},
keywords = {Stein manifolds; holomorphic submersions; Oka principle},
language = {eng},
number = {6},
pages = {1913-1942},
publisher = {Association des Annales de l'Institut Fourier},
title = {Holomorphic submersions from Stein manifolds},
url = {http://eudml.org/doc/116164},
volume = {54},
year = {2004},
}
TY - JOUR
AU - Forstnerič, Franc
TI - Holomorphic submersions from Stein manifolds
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 6
SP - 1913
EP - 1942
AB - We establish the homotopy classification of holomorphic submersions from Stein manifolds
to Complex manifolds satisfying an analytic property introduced in the paper. The result
is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.
LA - eng
KW - Stein manifolds; holomorphic submersions; Oka principle
UR - http://eudml.org/doc/116164
ER -
References
top- R. Abraham, Transversality in manifolds of mappings., Bull. Amer. Math. Soc. 69 (1963), 470-474 Zbl0171.44501MR149495
- W. Barth, C. Peters, A. Van De Ven, Compact Complex Surfaces, (1984), Springer, Berlin--Heidelberg--New Zork--Tokyo Zbl0718.14023MR749574
- J.-P Demailly, Cohomology of -convex spaces in top degrees, Math. Z. 204 (1990), 283-295 Zbl0682.32017MR1055992
- F. Docquier, H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten. (German), Math. Ann. 140 (1960), 94-123 Zbl0095.28004MR148939
- Y. Eliashberg, Topological characterization of Stein manifolds of dimension , Internat. J. Math 1 (1990), 29-46 Zbl0699.58002MR1044658
- Y. Eliashberg, N. Mishachev, Introduction to the -principle, 48 (2002), Amer. Math. Soc., Providence, RI Zbl1008.58001MR1909245
- O. Forster, Plongements des variétés de Stein, Comment. Math. Helv 45 (1970), 170-184 Zbl0184.31403MR269880
- F. Forstnerič, Noncritical holomorphic functions on Stein manifolds, Acta Math. 191 (2003), 143-189 Zbl1064.32021MR2051397
- F. Forstnerič, The homotopy principle in complex analysis: A survey, Explorations in Complex and Riemannian Geometry: A Volume dedicated to Robert E. Greene 332 (2003), 73-99, American Mathematical Society, Providence Zbl1048.32004
- F. Forstnerič, The Oka principle for sections of subelliptic submersions, Math. Z. 241 (2002), 527-551 Zbl1023.32008MR1938703
- F. Forstnerič, Runge approximation on convex sets implies the Oka property, (February 2004) Zbl1103.32004
- F. Forstnerič, J. Kozak, Strongly pseudoconvex handlebodies., J. Korean Math. Soc. 40 (2003), 727-746 Zbl1044.32025MR1995074
- F. Forstnerič, E. Low, N. Øvrelid, Solving the - and -equations in thin tubes and applications to mappings., Michigan Math. J. 49 (2001), 369-416 Zbl1016.32018MR1852309
- F. Forstnerič, J. Prezelj, Oka's principle for holomorphic fiber bundles with sprays., Math. Ann. 317 (2000), 117-154 Zbl0964.32017MR1760671
- F. Forstnerič, J. Prezelj, Oka's principle for holomorphic submersions with sprays., Math. Ann. 322 (2002), 633-666 Zbl1011.32006MR1905108
- F. Forstnerič, J. Prezelj, Extending holomorphic sections from complex subvarieties., Math. Z. 236 (2001), 43-68 Zbl0968.32005MR1812449
- F. Forstnerič, J.-P. Rosay, Approximation of biholomorphic mappings by automorphisms of ., Invent. Math. 112 (1993), 323-349 Zbl0792.32011MR1213106
- H. Grauert, Approximationssätze für holomorphe Funktionen mit Werten in komplexen Räumen., Math. Ann. 133 (1957), 139-159 Zbl0080.29201MR98197
- H. Grauert, Holomorphe Funktionen mit Werten in komplexen Lieschen Gruppen., Math. Ann. 133 (1957), 450-472 Zbl0080.29202MR98198
- H. Grauert, Analytische Faserungen über holomorph-vollständigen Räumen., Math. Ann. 135 (1958), 263-273 Zbl0081.07401MR98199
- M. Gromov, Stable maps of foliations into manifolds., Izv. Akad. Nauk, S.S.S.R 33 (1969), 707-734 Zbl0197.20404MR263103
- M. Gromov, Convex integration of differential relations, I, Izv. Akad. Nauk SSSR Ser. Mat (Russian) 37 (1973), 329-343 Zbl0254.58001MR413206
- M. Gromov, Partial Differential Relations., 9 (1986), Springer, Berlin--New York Zbl0651.53001MR864505
- M. Gromov, Oka's principle for holomorphic sections of elliptic bundles., J. Amer. Math. Soc. 2 (1989), 851-897 Zbl0686.32012MR1001851
- R. C. Gunning, R. Narasimhan, Immersion of open Riemann surfaces., Math. Ann. 174 (1967), 103-108 Zbl0179.11402MR223560
- R. C. Gunning, H. Rossi, Analytic functions of several complex variables., (1965), Prentice--Hall, Englewood Cliffs Zbl0141.08601MR180696
- G. M. Henkin, J. Leiterer, Andreotti-Grauert Theory by Integral Formulas., 74 (1988), Birkhäuser, Boston Zbl0654.32002MR986248
- G. M. Henkin, J. Leiterer, The Oka-Grauert principle without induction over the basis dimension., Math. Ann. 311 (1998), 71-93 Zbl0955.32019MR1624267
- L. Hörmander, estimates and existence theorems for the operator., Acta Math. 113 (1965), 89-152 Zbl0158.11002MR179443
- L. Hörmander, An Introduction to Complex Analysis in Several Variables, (1990), North Holland, Amsterdam Zbl0685.32001MR1045639
- L. Hörmander, J. Wermer, Uniform approximations on compact sets in ., Math. Scand 23 (1968), 5-21 Zbl0181.36201MR254275
- K. Oka, Sur les fonctions des plusieurs variables. III: Deuxième problème de Cousin., J. Sc. Hiroshima Univ. 9 (1939), 7-19 Zbl0020.24002
- A. Phillips, Submersions of open manifolds., Topology 6 (1967), 170-206 Zbl0204.23701MR208611
- R. M. Range, Y. T. Siu, approximation by holomorphic functions and -closed forms on submanifolds of a complex manifold., Math. Ann. 210 (1974), 105-122 Zbl0275.32008MR350068
- J.-P. Rosay, A counterexample related to Hartog’s phenomenon (a question by E. Chirka)., Michigan Math. J. 45 (1998), 529-535 Zbl0960.32020MR1653267
- J.-T. Siu, Every Stein subvariety admits a Stein neighborhood., Invent. Math. 38 (1976), 89-100 Zbl0343.32014MR435447
- J. Winkelman, The Oka-principle for mappings between Riemann surfaces., Enseign. Math. (2) 39 (1993), 143-151 Zbl0783.30031MR1225261
- F. Forstnerič, J.-P. Rosay, Approximation of biholomorphic mappings by automorphisms of , Invent. Math. (Erratum) 118 (1994), 573-574 Zbl0808.32017MR1296357
- M. Gromov, Convex integration of differential relations, I, Math. USSR--Izv. (English translation) 7 (1973), 329-343 Zbl0281.58004MR413206
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.