Equivariant Oka theory: survey of recent progress.
Publisher DOI
PubMed ID
36034193
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 , all over a reduced Stein space X with compatible actions of a reductive complex group on E, , 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.
Date Issued
2022-08-24
Publication Type
Article
Subject(s)
Subjects
Elliptic manifold Geometric invariant theory Lie group Linearisation problem Oka manifold Oka principle Oka theory Principal bundle Reductive group
Language(s)
en
Author(s)
Lárusson, Finnur | |
Schwarz, Gerald W |
Additional Credits
Journal
Complex analysis and its synergies
Publisher
Springer
ISSN
2197-120X
Access(Rights)
open.access