Equivariant Oka theory: survey of recent progress.

Autor: Kutzschebauch F; Institute of Mathematics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland., Lárusson F; School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005 Australia., Schwarz GW; Department of Mathematics, Brandeis University, Waltham, MA 02454-9110 USA.
Jazyk: angličtina
Zdroj: Complex analysis and its synergies [Complex Analysis Synerg] 2022; Vol. 8 (3), pp. 15. Date of Electronic Publication: 2022 Aug 24.
DOI: 10.1007/s40627-022-00103-5
Abstrakt: 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.
(© The Author(s) 2022.)
Databáze: MEDLINE
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