A solution of Gromov's Vaserstein problem

Ivarsson, Björn; Kutzschebauch, Frank

doi:10.1016/j.crma.2008.10.017

Cited by 10 publications

(9 citation statements)

References 20 publications

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“…The results of the present paper have been announced in Comptes Rendus [16], communicated by Misha Gromov. The authors like to thank him for his interest in the subject.…”

Section: G])mentioning

confidence: 73%

Holomorphic factorization of mappings into SL_n(C)

Ivarsson

Kutzschebauch

2012

Ann. Math.

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“…The results of the present paper have been announced in Comptes Rendus [16], communicated by Misha Gromov. The authors like to thank him for his interest in the subject.…”

Section: G])mentioning

confidence: 73%

Holomorphic factorization of mappings into SL_n(C)

Ivarsson

Kutzschebauch

2012

Ann. Math.

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“…(ii) A stratified subelliptic submersion, or a stratified holomorphic fiber bundle with Oka fibers, is an Oka map if and only if it is a Serre fibration. Corollary 1.2 (i) and the proof by Ivarsson and Kutzschebauch [8] gives the following solution of the parametric Gromov-Vaserstein problem [7,12]. Theorem 1.5.…”

Section: Question 13 Does Every Holomorphic Submersion With Oka Fiber...mentioning

confidence: 87%

Oka maps

Forstnerič

2009

Comptes Rendus. Mathématique

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Given a holomorphic submersion of reduced complex spaces, we prove that the basic Oka property of the submersion implies the parametric Oka property. This generalizes the corresponding result for complex manifolds (F. Forstneric, Oka Manifolds, C. R. Acad. Sci. Paris, Ser. I, 347 (2009) 1017-1020). It follows that a stratified elliptic (or subelliptic) holomorphic submersion, or a stratified holomorphic fiber bundle whose fibers are Oka manifolds, enjoys the parametric Oka property. As an application we give a parametric version of the factorization theorem due to Ivarsson and Kutzschebauch (A solution of Gromov's Vaserstein problem, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 1239-1243) for holomorphic maps from finite dimensional reduced Stein spaces to the special linear group SL_n(C)

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“…This is the so called Vaserstein problem posed by Gromov in [26]. Although it was recently solved by Ivarsson and the first author [29], [30] we will restrict ourselves to the present simple version of our lemma since it is fully sufficient for the purpose of the present paper.…”

Section: From Lemma 73 We Get Proposition 22mentioning

confidence: 98%

Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

Kutzschebauch¹,

Lodin²

2013

Duke Math. J.

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Abstract. We construct holomorphic families of proper holomorphic embeddings of C k into C n (0 < k < n− 1), so that for any two different parameters in the family no holomorphic automorphism of C n can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of C n we derive the existence of families of holomorphic C * -actions on C n (n ≥ 5) so that different actions in the family are not conjugate. This result is surprising in view of the long standing Holomorphic Linearization Problem, which in particular asked whether there would be more than one conjugacy class of C * actions on C n (with prescribed linear part at a fixed point).

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A solution of Gromov's Vaserstein problem

Cited by 10 publications

References 20 publications

Holomorphic factorization of mappings into SL_n(C)

Holomorphic factorization of mappings into SL_n(C)

Oka maps

Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

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