The first thirty years of Andersén-Lempert theory. (English) Zbl 1524.32023
Summary: In this paper we expose the impact of the fundamental discovery, made by E. Andersén and L. Lempert [Invent. Math. 110, No. 2, 371–388 (1992; Zbl 0770.32015)], that the group generated by shears is dense in the group of holomorphic automorphisms of a complex Euclidean space of dimension \(n > 1\). In three decades since its publication, their groundbreaking work led to the discovery of several new phenomena and to major new results in complex analysis and geometry involving Stein manifolds and affine algebraic manifolds with many automorphisms. The aim of this survey is to present the focal points of these developments, with a view towards the future.
MSC:
| 32M17 | Automorphism groups of \(\mathbb{C}^n\) and affine manifolds |
| 32Q56 | Oka principle and Oka manifolds |
| 14R10 | Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) |
| 53D35 | Global theory of symplectic and contact manifolds |
Citations:
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