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Title: Structures on foliations
Author: Harrison, Jenny
ISNI:       0000 0001 3538 9261
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1975
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In this thesis we consider various structures on foliations. In Chapter I we look at PL and topological foliations and note that not every topological foliation can he made PL. We show that every proper leaf has a microbundle normal to the foliation with holonomy structure group. For transverse foliations the fibres can be chosen not only normal to the leaves of the foliation containing the base leaf, but contained in the leaves of the other foliation. Thus normal microbundles are unique up to isotopy. We also look into the relationship between the holonony group and the foliated neighbourhood of a leaf. In Chapter II we study differentiable structures on foliations, showing that differentiability conditions are meaningful in a topological sense. We do this by constructing an example of a Cr foliation which is not homeomorphic to any Cr+1 foliation, r > 0. (The example is the suspension of a diffeomorphism of a two-manifold.) Using results from Chapter I we also show that the foliation is not Cs integrably homotopic to any Cr+1 foliation, 0 < s < r.
Supervisor: Not available Sponsor: Marshall Aid Commemoration Commission
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics