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dc.contributor.advisorVarghese, Mathai-
dc.contributor.advisorThiang, Guo Chuan-
dc.contributor.advisorWang, Hang-
dc.contributor.authorLim, Johnny-
dc.description.abstractLet X be a smooth compact manifold. We propose a geometric model for the group K⁰(X,R/Z): We study a well-defined and non-degenerate analytic duality pairing between K⁰(X,R/Z) and its Pontryagin dual group, the Baum-Douglas geometric K-homology K₀(X); whose pairing formula comprises of an analytic term involving the Dai-Zhang eta-invariant associated to a twisted Dirac-type operator and a topological term involving a differential form and some characteristic forms. This yields a robust R/Z-valued invariant. We also study two special cases of the analytic pairing of this form in the cohomology groups H¹(X,R/Z) and H²(X,R/Z):en
dc.subjectR/Z K-Theoryen
dc.subjectDai-Zhang Index theoremen
dc.subjectanalytic pairingen
dc.titleAnalytic Pontryagin Dualityen
dc.contributor.schoolSchool of Mathematical Sciencesen
dc.provenanceThis 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:
dc.description.dissertationThesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2019en
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