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DC Field | Value | Language |
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dc.contributor.advisor | Larusson, Finnur | en |
dc.contributor.advisor | Buchdahl, Nicholas | en |
dc.contributor.author | Crawford, William | en |
dc.date.issued | 2014 | en |
dc.identifier.uri | http://hdl.handle.net/2440/84514 | - |
dc.description.abstract | In his 1993 paper, J. Winkelmann determined the precise pairs of Riemann surfaces for which every continuous map between them can be deformed to a holomorphic map. In particular, it is true for all maps from non-compact Riemann surfaces into C, C*, the Riemann sphere or complex tori. This is a result of M. Gromov's seminal paper in 1989, where he introduced elliptic manifolds and showed that every continuous map from a Stein manifold into an elliptic manifold can be deformed to a holomorphic map. The elliptic Riemann surfaces are C, C*, the Riemann sphere and complex tori. Gromov incorporated versions of the Weierstrass and Runge approximation theorems into the deformation to get stronger Oka properties, known as BOPAI and BOPAJI in the literature. It has since been shown, using deep, higher dimensional techniques, that maps from Stein manifolds into elliptic manifolds satisfy BOPAI and BOPAJI. In this thesis we strengthen Winkelmann's results to find the precise pairs of Riemann surfaces that satisfy the stronger Oka properties of BOPAI and BOPAJI. We rely on Riemann surface theory, Morse theory and algebraic topology, rather than techniques from higher dimensional complex analysis. | en |
dc.subject | Oka theory; Riemann surfaces; hyperbolicity theory; homotopy theory | en |
dc.title | Oka theory of Riemann surfaces. | en |
dc.type | Thesis | en |
dc.contributor.school | School of Mathematical Sciences | en |
dc.provenance | 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/legals | en |
dc.description.dissertation | Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2014 | en |
Appears in Collections: | Research Theses |
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02whole.pdf | 613.16 kB | Adobe PDF | View/Open | |
Permissions Restricted Access | Library staff access only | 238.71 kB | Adobe PDF | View/Open |
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