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I have created a new lead which is much more comprehensive, and most importantly, not wrong, as the old lead was. If it is too expansive then the content should be moved into a section about classification, rather than simply deleted. As it is right now I would say it is at the limit of what could be
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I would like hear why symplectic topology/geometry is categorized under differential topology instead of differential geometry. Should not differential topology deal only with structures that can be naturally built upon any smooth manifold? Of course the cotangent bundle of any smooth manifold has a
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Nevertheless, the distinction becomes clearer in abstract terms. Differential topology is the study of the (infinitesimal, local, and global) properties of structures on manifolds having no non-trivial local moduli, whereas differential geometry is the study of the (infinitesimal, local, and global)
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The culmination of the 'Differential topology versus differential geometry' section indicates that the difference between differential topology and differential geometry comes down to the presence or absence of 'local moduli'. I interpreted this to mean that the space is in fact a
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natural symplectic structure, but the base manifold itself has not. As far as I understand, two different symplectic structures on the same base manifold are not necessarily symplectomorphic, so a symplectic form is a genuine geometric structure.
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Apparently a great many editors seem to feel that mathematicians should generally be referred to by the masculine pronoun "he". If there is consensus on
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to reflect this fact. Until that time, however, any change in the pronoun "she" to "he" without providing a valid reason is likely to be reverted.
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As you see, "differential topology" and "differential geometry" is the study of the same thing. --
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properties of structures on manifolds having non-trivial local moduli.
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