1. Equivariant Oka theory: Survey of recent progress
- Author
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Kutzschebauch, Frank, Larusson, Finnur, and Schwarz, Gerald W.
- Subjects
Mathematics - Complex Variables ,Mathematics - Algebraic Geometry ,Mathematics - Representation Theory ,Primary 32M05. Secondary 14L24, 14L30, 32E10, 32E30, 32M10, 32M17, 32Q28, 32Q56 - 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 $\mathscr G$, all over a reduced Stein space $X$ with compatible actions of a reductive complex group on $E$, $\mathscr G$, 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 new notion of a $G$-manifold being $G$-Oka., Comment: arXiv admin note: text overlap with arXiv:1612.07372
- Published
- 2021