Abstract
In this chapter we study holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups, a subject closely intertwined with Oka theory. The main focus of the chapter is on the Andersén-Lempert theory and its generalization to complex manifolds satisfying Varolin’s density property. Applications include the construction of nonstraightenable embedded complex lines, of twisted proper holomorphic embeddings of Stein spaces into Euclidean spaces, of nonlinearizable periodic holomorphic automorphisms of ℂn, of non-Runge Fatou-Bieberbach domains, and of non-Stein fiber bundles over the disc or the plane whose transition maps are polynomial automorphisms of the fiber ℂ2.
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© 2011 Springer-Verlag Berlin Heidelberg
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Forstnerič, F. (2011). Automorphisms of Complex Euclidean Spaces. In: Stein Manifolds and Holomorphic Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22250-4_4
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DOI: https://doi.org/10.1007/978-3-642-22250-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22249-8
Online ISBN: 978-3-642-22250-4
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