Holomorphic factorization of mappings into SL_n(C)

Ivarsson, Björn; Kutzschebauch, Frank

doi:10.4007/annals.2012.175.1.3

Cited by 34 publications

(30 citation statements)

References 25 publications

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“…Theorem 3 (Ivarsson and Kutzschebauch [IK12]). Let W be a finite dimensional reduced Stein space and G : W → SL n (C) be a nullhomotopic holomorphic mapping.…”

Section: Introductionmentioning

confidence: 99%

Parametric jet interpolation for Stein manifolds with the density property

Ramos-Peon

Ugolini

2019

Int. J. Math.

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“…Theorem 3 (Ivarsson and Kutzschebauch [IK12]). Let W be a finite dimensional reduced Stein space and G : W → SL n (C) be a nullhomotopic holomorphic mapping.…”

Section: Introductionmentioning

confidence: 99%

Parametric jet interpolation for Stein manifolds with the density property

Ramos-Peon

Ugolini

2019

Int. J. Math.

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“…An analogous result was proved recently by Ivarsson and Kutzschebauch [20] for holomorphic matrices on a finite-dimensional reduced Stein space (so-called Gromov's Vaserstein problem). The number of factors of the required factorization in their theorem depends only on n and the dimension of the Stein space.…”

Section: Preliminaries On Banach Algebrasmentioning

confidence: 55%

Projective free algebras of continuous functions on compact abelian groups

Brudnyi¹,

Rodman²,

Spitkovsky³

2010

Journal of Functional Analysis

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It is proved that the Wiener algebra of functions on a connected compact abelian group whose BohrFourier spectra are contained in a fixed subsemigroup of the (additive) dual group, is projective free. The semigroup is assumed to contain zero and have the property that it does not contain both a nonzero element and its opposite. The projective free property is proved also for the algebra of continuous functions with the same condition on their Bohr-Fourier spectra. As an application, the connected components of the set of factorable matrices are described. The proofs are based on a key result on homotopies of continuous maps on the maximal ideal spaces of the algebras under consideration.

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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: 99%

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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Holomorphic factorization of mappings into SL_n(C)

Abstract: We solve Gromov's Vaserstein problem. Namely, we show that a nullhomotopic holomorphic mapping from a finite dimensional reduced Stein space into SLn(C) can be factored into a finite product of unipotent matrices with holomorphic entries.

Cited by 34 publications

References 25 publications

Parametric jet interpolation for Stein manifolds with the density property

Parametric jet interpolation for Stein manifolds with the density property

Projective free algebras of continuous functions on compact abelian groups

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

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