Harrison, Jenny (1975) Structures on foliations. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Foliations (Mathematics)
Official Date:	May 1975
Dates:	Date Event May 1975 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Rourke, C. P. (Colin Patrick)
Sponsors:	Marshall Aid Commemoration Commission
Extent:	39 leaves
Language:	eng

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