An equivariant parametric Oka principle for bundles of homogeneous spaces
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 ,...
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Published in | Mathematische annalen Vol. 370; no. 1-2; pp. 819 - 839 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2018
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0025-5831 1432-1807 |
DOI: | 10.1007/s00208-017-1588-1 |