Bundles and morphisms between bundles are defined in the category of
Fr¨olicher spaces (earlier known as the category of smooth spaces, see [2], [5],
[9], [6] and [7]). We show that the sections of Fr¨olicher bundles are Fr¨olicher
smooth maps and the fibers of Fr¨olicher bundles have a Fr¨olicher structure.
We prove in detail that the tangent and cotangent bundles of a n-dimensional
pseudomanifold are locally diffeomorphic to the even-dimensional Euclidian
canonical F-space R2n. We define a bilinear form on a finite-dimensional
pseudomanifold. We show that the symplectic structure on a cotangent bundle
in the category of Fr¨olicher spaces exists and is (locally) obtained by the
pullback of the canonical symplectic structure of R2n. We define the notion
of symplectomorphism between two symplectic pseudomanifolds. We prove
that two cotangent bundles of two diffeomorphic finite-dimensional pseudomanifolds
are symplectomorphic in the category of Frölicher spaces.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/5860 |
| Date | 02 December 2008 |
| Creators | Toko, Wilson Bombe |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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