Homology and homotopy of infinite dimensional manifolds

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dc.contributor.committeeMemberBourgin, David G.
dc.contributor.committeeMemberWhitman, Andrew P.
dc.contributor.committeeMemberFulp, Ronald O.
dc.contributor.committeeMemberYoes, M. G., Jr.
dc.contributor.committeeMemberSchmidt, Jürgen
dc.creatorMartens, Phillip Arthur
dc.date.accessioned2022-06-22T13:40:57Z
dc.date.available2022-06-22T13:40:57Z
dc.date.issued1969
dc.description.abstractThis paper is concerned with a study of the structure of infinite dimensional manifolds, giving information about the homology and homotopy, and leading to the construction of a codimensional homology functor which distinguishes sets of finite codimension and which satisfies a Poincare duality with respect to the singular cohomology. Attention is restricted to separable differentiable Hilbert manifolds which are Cauchy and geodesically complete and which support finite dimensional vector valued functions with associated thin singular sets so that these sets can be removed via diffeomorphisms between the manifolds and the complements of the thin subsets. This leads to representations for these manifolds as the inverse limit of finite dimensional manifolds which are the Images of the given manifold under a vector valued function, with the structure of the inverse system being determined by a sequence of foliations and an associated sequence of q-parameter groups of diffeomorphisms. There is also a strong homotopy equivalence between the given infinite dimensional manifold and the direct limit of the above mentioned finite dimensional manifolds, A homology functor H[lowered infinity-p] (•,Z) is then constructed by using the strong homotopy equivalence and the connecting homomorphisms of Mayer-Vletoros exact sequences which arise from splittings of the finite dimensional manifolds used In the representations. The ensuing duality is independent of any representation.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13655318
dc.identifier.urihttps://hdl.handle.net/10657/9764
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleHomology and homotopy of infinite dimensional manifolds
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Arts and Sciences
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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