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Type: Journal article
Title: Gromov’s Oka principle for equivariant maps
Author: Kutzschebauch, F.
Lárusson, F.
Schwarz, G.W.
Citation: Journal of Geometric Analysis, 2020; OnlinePubl:1-26
Publisher: Springer
Issue Date: 2020
ISSN: 1050-6926
Statement of
Frank Kutzschebauch, Finnur Lárusson and Gerald W. Schwarz
Abstract: We take the first step in the development of an equivariant version of modern, Gromov-style Oka theory. We define equivariant versions of the standard Oka property, ellipticity, and homotopy Runge property of complex manifolds, show that they satisfy all the expected basic properties, and present examples. Our main theorem is an equivariant Oka principle saying that if a finite group G acts on a Stein manifold X and another manifold Y in such a way that Y is G-Oka, then every G-equivariant continuous map X→Y can be deformed, through such maps, to a G-equivariant holomorphic map. Approximation on a G-invariant holomorphically convex compact subset of X and jet interpolation along a G-invariant subvariety of X can be built into the theorem. We conjecture that the theorem holds for actions of arbitrary reductive complex Lie groups and prove partial results to this effect.
Description: OnlinePubl Published: 25 September 2020
Rights: Copyright © 2020, Mathematica Josephina, Inc.
RMID: 1000026872
DOI: 10.1007/s12220-020-00520-0
Grant ID:
Appears in Collections:Physics publications

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