Equivariant Oka theory: survey of recent progress

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...

Full description

Saved in:
Bibliographic Details
Published in:Complex analysis and its synergies 2022, Vol.8 (3), p.15-15, Article 15
Main Authors: Kutzschebauch, Frank, Lárusson, Finnur, Schwarz, Gerald W.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Functions of a Complex Variable
Isomorphism
Lie groups
Manifolds
Mappings and symmetry in complex and CR geometry
Mathematics
Mathematics and Statistics
Partial Differential Equations
Principles
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 G , all over a reduced Stein space X with compatible actions of a reductive complex group on E , G , 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 notion of a G -manifold being G -Oka.
ISSN:2524-7581
2197-120X
DOI:10.1007/s40627-022-00103-5