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nLab > Latest Changes: Wu manifold

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  1. Created stub for Wu manifold, which is now linked on rational homology sphere.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2024

    have added links to SU(3), SO(3) and coset space.

    also renamed the Examples-section to “Properties” and its “Example” to a “Proposition”.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorSamuel Adrian Antz
    • CommentTimeMay 31st 2024
    • (edited May 31st 2024)

    Added another important property of the Wu manifold: It allows a spin^h structure, but no spin^c strucutre.

    diff, v3, current

  4. Added cohomology groups (with coefficients in ℤ 2\mathbb{Z}_2) and the Wu manifold generating the oriented bordism ring Ω 5 SO≅ℤ 2\Omega_5^{\operatorname{SO}}\cong\mathbb{Z}_2 together with two references. Linked new english Wikipedia page. (The german Wikipedia page is now also available.)

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorSamuel Adrian Antz
    • CommentTimeJul 19th 2024
    • (edited Jul 19th 2024)

    Added some properties of the Wu manifold. So far, I have no references for them yet, but Diarmuid Crowley (whose 5-manifolds: 1-connected I’ve already added in the references) told them to me in person, when he visited the University of Augsburg on Monday.

    Also replaced “spin^h” and “spin^c” by “spinʰ” and “spinᶜ”, see discussion here.

    diff, v6, current

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