2026-09-21T13:16:45Zhttps://digital.library.adelaide.edu.au/server/oai/request

oai:digital.library.adelaide.edu.au:2440/998942026-06-12T08:31:07Zcom_2440_14759col_2440_14760

Larusson, Finnur Buchdahl, Nicholas Chenoweth, Brett Simon School of Mathematical Sciences 2016 http://hdl.handle.net/2440/99894 A fundamental property of an Oka manifold Y is that every continuous map from a Stein manifold X to Y can be deformed to a holomorphic map. In a recent paper, Larusson [19] considers the natural question of whether it is possible to simultaneously deform all continuous maps f from X to Y to holomorphic maps, in a way that depends continuously on f and does not change f if f is holomorphic to begin with. In other words, is 𝒪(X, Y ) a deformation retract of 𝒞 (X, Y )? Larusson provided a partial answer to this question. In this thesis we further develop the work of Larusson on the topological relationship between spaces of continuous maps and spaces of holomorphic maps from Stein manifolds to Oka manifolds, mainly in the context of domains in ℂ. The main tools we use come from complex analysis, Oka theory, algebraic topology and the theory of absolute neighbourhood retracts. One of our main results provides a large supply of infinitely connected domains X in ℂ such that 𝒪(X, ℂ*) is a deformation retract of 𝒞 (X, ℂ*). Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2016. Deformation retractions spaces continuous maps holomorphic maps Deformation retractions from spaces of continuous maps onto spaces of holomorphic maps Theses This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legalsopen.access