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dc.contributor.advisorBraden, Harryen
dc.contributor.advisorGordon, Iainen
dc.contributor.authorDocherty, Pamela Janeen
dc.date.accessioned2013-09-25T10:57:05Z
dc.date.available2013-09-25T10:57:05Z
dc.date.issued2012-11-28
dc.identifier.urihttp://hdl.handle.net/1842/7838
dc.description.abstractA current group GX is an infinite-dimensional Lie group of smooth maps from a smooth manifold X to a finite-dimensional Lie group G, endowed with pointwise multiplication. This thesis concerns current groups G§ for compact Riemann surfaces §. We extend some results in the literature to discuss the topology of G§ where G has non-trivial fundamental group, and use these results to discuss the theory of central extensions of G§. The second object of interest in the thesis is the Jacobi group, which we think of as being associated to a compact Riemann surface of genus one. A connection is made between the Jacobi group and a certain central extension of G§. Finally, we define a generalisation of the Jacobi group that may be thought of as being associated to a compact Riemann surface of genus g ≥ 1.en
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en
dc.language.isoen
dc.publisherThe University of Edinburghen
dc.subjectcentral extensionsen
dc.subjectcurrent groupsen
dc.subjectJacobien
dc.titleCentral extensions of Current Groups and the Jacobi Groupen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


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