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nLab > Latest Changes: MSU

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2020

    starting something

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020
    • (edited Nov 20th 2020)

    added this pointer:

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added pointer to:

    • Taras Panov, A geometric view on SU-bordism, talk at Moscow State University 2020 (webpage, pdf)

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020
    • (edited Nov 20th 2020)

    added the statement that

    the SU-bordism ring is spanned by classes of Calabi-Yau manifolds: in particular the K3 surface in degree 4 and certain CY 3-folds and CY4-folds in degrees 6 and 8.

    Will give this statement its own little entry now (Calabi-Yau manifolds in SU-bordism theory), for ease of cross-linking in the entries K3 surface and Calabi-Yau manifold

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added pointer to:

    • Pierre Conner, Edwin Floyd, Torsion in SU-bordism, Memoirs of the American Mathematical Society 1966 (ISBN:978-1-4704-0007-1)

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added these statements:

    The kernel of the forgetful morphism

    ΩSU•⟶ΩU•

    from the SU-bordism ring to the complex bordism ring, is pure torsion.

    Every torsion element in the SU-bordism ring ΩSU• has order 2.

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    and this one:

    The torsion subgroup of the SU-bordism ring is concentrated in degrees 8k+1 and 8k+2, for k∈ℕ.

    diff, v3, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2021

    added pointer to:

    diff, v7, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2021
    • (edited Feb 18th 2021)

    I have made explicit the corollary (here) that the image of the element [K3] of ΩSU4 is still non-trivial in ΩU4.

    (This must be well-known, but I have trouble finding a reference that says it more directly. A half-sentence in Novikov 86, p. 216 (218 of 321) suggests this, without, however, really saying so, much less proving it.)

    diff, v10, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2021

    added pointer to:

    for (the failure of) the Conner-Floyd isomorphism for MSU→KO.

    diff, v11, current

1 to 10 of 10

  1.