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Title: A Study Of Spacetime Topologies
Researcher: Sinha, Soami Pyari
Guide(s): Agarwal, Gunjan
Keywords: Physical Sciences,Mathematics,Mathematics
University: Dayalbagh Educational Institute
Completed Date: 2017
Abstract: Ideas of defining non-manifold topologies on flat and curved spacetime taking into account the causal structure of spacetime, paved the way for the use of topology in general relativity. The A, f, s, fine, t and space topologies are some of the topologies defined on Minkowski space and the path topology, space topology, separating topology, Zeeman topology and geodesic topology are some of the non-manifold topologies defined on Lorentz manifolds with a reasonable homeomorphism group making these topologies physically significant and interesting for their mathematical study. The work carried out in the present thesis revolves around a topological study of various physically relevant non-manifold topologies on Lorentz manifolds. newlineIn the present thesis, it is obtained that the Minkowski space with the A-topology is Hausdorff, path connected, separable, non-first countable, non-regular, non-compact and non-simply connected. It is also found that a set is compact in Minkowski space with the A-topology if and only if it is compact in the Euclidean space and does not contain the image of a Zeno sequence. The A-topology on the Minkowski space has been generalized to Lorentz manifolds and studied its compact sets and topological properties. newlineFurther, it is obtained that the homeomorphism group of Minkowski space with the f-topology is the group generated by Lorentz transformations together with translations and dilatations. It is obtained that the nonempty open sets of different dimensional Minkowski spaces with each of the fine topology, A-topology, s-topology, space topology and f-topology are not homeomorphic. These results are obtained for the Zeeman topology. This leads to the introduction of locally Minkowskian manifolds in the context of the fine and t-topologies. newlineExponential map has been obtained to be non-continuous for path, geodesic, space, separating and Zeeman topologies. Topological properties of a Lorentz manifold with each of the geodesic and Zeeman topologies have also been studied and obtained. newline
Appears in Departments:Department of Mathematics

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02_certificate.pdf82.43 kBAdobe PDFView/Open
03_declaration.pdf44.68 kBAdobe PDFView/Open
04_abstract.pdf84.05 kBAdobe PDFView/Open
05_acknowledgement.pdf86.59 kBAdobe PDFView/Open
06_contents.pdf273.62 kBAdobe PDFView/Open
07_list_of_figures.pdf80.75 kBAdobe PDFView/Open
08_preface.pdf84.5 kBAdobe PDFView/Open
09_chapter 1.pdf30.38 kBAdobe PDFView/Open
10_chapter 2.pdf290.55 kBAdobe PDFView/Open
11_chapter 3.pdf30.3 kBAdobe PDFView/Open
12_chapter 4.pdf143 kBAdobe PDFView/Open
13_chapter 5.pdf95.58 kBAdobe PDFView/Open
14_chapter 6.pdf58.3 kBAdobe PDFView/Open
15_chapter 7.pdf83.34 kBAdobe PDFView/Open
16_chapter 8.pdf49.77 kBAdobe PDFView/Open
17_chapter 9.pdf76.33 kBAdobe PDFView/Open
18_conclusion.pdf35.38 kBAdobe PDFView/Open
19_references.pdf30.7 kBAdobe PDFView/Open
20_appendix.pdf23.5 kBAdobe PDFView/Open
21_summary.pdf109.45 kBAdobe PDFView/Open

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