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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 6th 2009

    Added to tangent bundle the discussion in the context of synthetic differential geometry.

    In that context I also restructured a bit and expanded the introduction slightly.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2017
    • (edited May 14th 2017)

    (…almost 8 years later…)

    I have started to fill in at Definitions in ordinary differential geometry – Geometric definition details of the classical construction.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2017
    • (edited Jun 7th 2017)

    Continued to spell out traditional elementary detail at Geometric definition. In particular more of a proof now that the tangent bundle of a differentiable manifold is itself a manifold.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2017
    • (edited Jun 7th 2017)

    I have re-arranged the sections at tangent bundle:

    • made all the various sections that existed subsections of the “Definition”-section (because all discuss alternative definitions)

    • merged what used to be three sections for “algebraic”, “geometric” and “physics” definition (this was not my idea) into a single section “Traditional definition

      (the “algebraic definition” via derivations is one of vector fields, not of the tangent bundle itself, hence hardly an alternative definition; and the “physics” definition via gluing is really the only definition there is: even if one describes the topology on TXT X in a way that it does not explicitly mention the gluing construction, it is the corresponding quotient topology and the gluing construction is arguably the most transparent way to understand that topology )