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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 19th 2019

    added this statement:

    Let XX be a closed smooth manifold of dimension 8 with Spin structure. If the frame bundle moreover admits G-structure for

    G=Spin(7)Spin(8) G = Spin(7) \hookrightarrow Spin(8)

    then the Euler class χ\chi, the second Pontryagin class p 2p_2 and the cup product-square (p 1) 2(p_1)^2 of the first Pontryagin class of the frame bundle/tangent bundle are related by

    8χ=4p 2(p 1) 2. 8 \chi \;=\; 4 p_2 - (p_1)^2 \,.

    diff, v5, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 15th 2020

    added pointer to

    • Robert Bryant, Metrics with Exceptional Holonomy, Annals of Mathematics Second Series, Vol. 126, No. 3 (Nov., 1987), pp. 525-576 (jstor:1971360)

    diff, v15, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 15th 2020

    added pointer to

    diff, v16, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 15th 2020

    added pointer to

    • Ya. V. Bazaikin, On the new examples of complete noncompact Spin(7)-holonomy metrics, Sib Math J 48, 8–25 (2007) (doi:10.1007/s11202-007-0003-7)

    diff, v18, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 16th 2024

    added pointer to:

    diff, v20, current