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dc.contributor.advisorParker, Phillip E.
dc.contributor.authorRyan, Justin M.
dc.date.accessioned2014-11-17T16:19:36Z
dc.date.available2014-11-17T16:19:36Z
dc.date.issued2014-05
dc.identifier.otherd14012
dc.identifier.urihttp://hdl.handle.net/10057/10941
dc.descriptionThesis (Ph.D.)-- Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
dc.description.abstractAn Ehresmann connection on a fiber bundle pi: E --> M is defined by prescribing a suitable horizontal subbundle H of the tangent bundle piT: TE --> E. For a horizontal bundle to be suitable, it must have a property called horizontal path lifting. This property ensures that the horizontal bundle determines a system of parallel transport between the fibers of E. The main result of this dissertation is a geometric characterization of the horizontal bundles on E that have horizontal path lifting, and hence are connections. In particular, it is shown that a horizontal bundle has horizontal path lifting if and only if its horizontal spaces are bounded away from the vertical spaces, uniformly along fibers of E. In order for a horizontal bundle to admit a system of parallel transport or have holonomy, it must be a connection. However, certain other geometric properties that are usually attributed to connections are actually properties of arbitrary horizontal bundles. These properties are studied in the case when E is either a vector bundle or tangent bundle, accordingly.
dc.format.extentix, 60 p.
dc.language.isoen_US
dc.publisherWichita State University
dc.rightsCopyright 2014 Justin M. Ryan
dc.subject.lcshElectronic dissertations
dc.titleGeometry of horizontal bundles and connections
dc.typeDissertation


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