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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2023

    started a subsection (here) on Atiyah Real vector bundles

    diff, v5, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2023
    • (edited Nov 9th 2023)

    Added to the example “real vector bundles as Real vector bundles” (here) a line saying that the equivalence continues to hold over varying base spaces.

    Then below that I added a Remark (here) that, in contrast, complex vector bundles over varying bases do \, not \, form a full subcategory of Real vector bundles over varing /2\mathbb{Z}/2-spaces — but they do form a full subcategory of “Real vector bundles equipped with complex structure”, where “complex structure” means endomorphisms (of Real vector bundles) squaring to 1-1.

    In this sense, the term “Real vector bundle” is quite apt.

    diff, v9, current