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Framed stratified sets in Morse theory
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LeBel, André (1996) Framed stratified sets in Morse theory. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b140262
Abstract
Let. / be a Morse function on a closed manifold M. In this thesis, we investigate the relations between the attaching maps in the CYV complex determined by /, and the moduli spaces of gradient flow lines of /, with respect to some Riemannian metric on M.
These moduli spaces are naturally framed submanifolds of the unstable spheres of the gradient flow. The set of moduli spaces contained in a given unstable sphere determines a stratification of this sphere. The unstable spheres are thus stratified sets, with framed strata. It is possible to associate to such a structure a homotopy class of maps with values in some CW complex. Thus, the framed moduli spaces determine maps and it is shown in this thesis that one can use them to construct the classical Morse CW complex associated to /.
Our main tools are stratified sets and transverse CW complexes. We give smooth versions of known results in the PL category. In particular, we establish a transversality result and a Pontryagin-Thom correspondence for maps from manifolds with faces to CW complexes.
As an application, we determine the cup product of successive critical points in terms of linking of moduli spaces of flow lines.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Morse theory, Stratified sets, Manifolds (Mathematics), Moduli theory | ||||
| Official Date: | March 1996 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Jones, John | ||||
| Sponsors: | Commonwealth Scholarship Commission in the United Kingdom | ||||
| Format of File: | |||||
| Extent: | 106 pages | ||||
| Language: | eng |
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