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Type: Journal article
Title: An equivariant parametric Oka principle for bundles of homogeneous spaces
Author: Kutzschebauch, F.
Lárusson, F.
Schwarz, G.
Citation: Mathematische Annalen, 2018; 370(1-2):819-839
Publisher: Springer
Issue Date: 2018
ISSN: 0025-5831
Statement of
Frank Kutzschebauch, Finnur Lárusson, Gerald W. Schwarz
Abstract: We prove a parametric Oka principle for equivariant sections of a holomorphic fibre bundle E with a structure group bundle G on a reduced Stein space X, such that the fibre of E is a homogeneous space of the fibre of G, with the complexification K(C) of a compact real Lie group K acting on X, G, and E. Our main result is that the inclusion of the space of K(C)-equivariant holomorphic sections of E over X into the space of K-equivariant continuous sections is a weak homotopy equivalence. The result has a wide scope; we describe several diverse special cases. We use the result to strengthen Heinzner and Kutzschebauch’s classification of equivariant principal bundles, and to strengthen an Oka principle for equivariant isomorphisms proved by us in a previous paper.
Rights: © Springer-Verlag GmbH Deutschland 2017
RMID: 0030076039
DOI: 10.1007/s00208-017-1588-1
Grant ID:
Appears in Collections:Mathematical Sciences publications

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