Gromov’s Oka Principle for Equivariant Maps
| Autor: | Finnur Larusson, Gerald W. Schwarz, Frank Kutzschebauch |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Conjecture Jet (mathematics) Mathematics::Complex Variables Homotopy 010102 general mathematics Holomorphic function Lie group 16. Peace & justice Mathematics::Algebraic Topology 01 natural sciences Manifold 0103 physical sciences Stein manifold Equivariant map 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | The Journal of Geometric Analysis. 31:6102-6127 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-020-00520-0 |
| Popis: | 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 $$X\rightarrow Y$$ 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. |
| Databáze: | OpenAIRE |
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