Equivariant Oka theory: Survey of recent progress

DOI10.1007/S40627-022-00103-5arXiv2112.03332MaRDI QIDQ6384962

Frank Kutzschebauch, Finnur Lárusson, Gerald W. Schwarz

Publication date: 6 December 2021

Abstract: We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group $G$ acts. Applications to the linearisation problem. A parametric Oka principle for sections of a bundle $E$ of homogeneous spaces for a group bundle $mathscrG$, all over a reduced Stein space $X$ with compatible actions of a reductive complex group on $E$, $mathscrG$, and $X$. Application to the classification of generalised principal bundles with a group action. Finally, an equivariant version of Gromov's Oka principle based on a new notion of a $G$-manifold being $G$-Oka.

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30) Complex Lie groups, group actions on complex spaces (32M05) Stein manifolds (32Q28) Stein spaces (32E10) Homogeneous complex manifolds (32M10) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30) Automorphism groups of (mathbb{C}^n) and affine manifolds (32M17) Oka principle and Oka manifolds (32Q56)

This page was built for publication: Equivariant Oka theory: Survey of recent progress

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6384962)