An equivariant parametric Oka principle for bundles of homogeneous spaces 12:10 Fri 3 Mar, 2017 :: Napier 209 :: Finnur Larusson :: University of Adelaide
I will report on new joint work with Frank Kutzschebauch and Gerald Schwarz (arXiv:1612.07372). Under certain conditions, every continuous section of a holomorphic fibre bundle can be deformed to a holomorphic section. In fact, the inclusion of the space of holomorphic sections into the space of continuous sections is a weak homotopy equivalence. What if a complex Lie group acts on the bundle and its sections? We have proved an analogous result for equivariant sections. The result has a wide scope. If time permits, I will describe some interesting special cases and mention two applications.