An equivariant parametric Oka principle for bundles of homogeneous spaces

Kutzschebauch, Frank; Larusson, Finnur; Schwarz, Gerald (2018). An equivariant parametric Oka principle for bundles of homogeneous spaces. Mathematische Annalen, 370(1-2), pp. 819-839. Springer 10.1007/s00208-017-1588-1

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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 Kℂ of a compact real Lie group K acting on X, G, and E. Our main result is that the inclusion of the space of Kℂ-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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Kutzschebauch, Frank; Larusson, Finnur and Schwarz, Gerald

Subjects:

500 Science > 510 Mathematics

ISSN:

0025-5831

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

15 May 2019 17:43

Last Modified:

24 Oct 2019 16:08

Publisher DOI:

10.1007/s00208-017-1588-1

BORIS DOI:

10.7892/boris.125527

URI:

https://boris.unibe.ch/id/eprint/125527

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