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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 10th 2022

    Idea

    Cup-i products extend cup products.

    They can be used to define Steenrod squares in the same manner as ordinary cup products can be used to define the square of a cohomology class.

    Definition

    Given a simplicial set X and i0, we define the cup-i product as the map on simplicial cochains on X with coefficients in Z/2 induced by the map on simplicial chains

    Δi:C(X,Z/2)C(X,Z/2)C(X,Z/2),

    where Δi evaluate on an n-simplex xXn is 0 if iUnknown charactern and

    UdU0(x)dU1(x),

    where U{0,,n} has cardinality ni and

    Uk={uUr(u)+k=u(mod2)},

    where r(u)=#{vUvu}.

    References

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 10th 2022

    I have added context menu and table of contents.

    Are you going to create the page Anibal M. Medina-Mardones? Please do, otherwise the broken links in the entry look bad.

    diff, v2, current