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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2012
    • (edited Dec 14th 2012)

    expanded the Idea- and the Definition section at G2-manifold (also further at G2). (Still not really complete, though.) Highlighted the relation to 2-plectic geometry and cross-linked there.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 4th 2013

    added a brief remark on weak G2 holonomy. Needs to be expanded…

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 12th 2015
    • (edited Jan 12th 2015)

    I have expanded a little at G2-structure, added the characterization via “definite” 3-forms, such as to then add a brief section on closed G2-structure – all following the nice note Bryant 05.

    The upshot is a remark that closed G 2G_2-structures are given by certain phased correspondences of cohesive homotopy types.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2015

    added to G2-manifold as an example discussion of how the “definite” 3-forms are given by contraction of the canonical one with vielbein fields.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2015

    just for those who check the logs and are wondering: I have been making minor edits and adding references to various entries, including G-structure, M-theory on G2-manifold, geometry of physics – supergeometry and probably others.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2015
    • (edited Dec 4th 2015)

    I spotted and now fixed an annoying typo in a cross-link at G2-manifold: at the crucial point where Bryant’s theorem was mentioned that closed and coclosed G 2G_2-structures (hence G 2G_2-manifold structures) are precisely the torsion-free G 2G_2-structures, the cross-reference pointed only to the closure-clause, not to the co-closure clause. I have fixed this now. Also added the statement of the equivalence to vanishing Ricci curvature.

    Finally I merged it all into one statement.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 28th 2017

    only now learned of Kovalev’s new (not so new anymore) construction of a new class of compact G 2G_2-manifolds. Added pointer at G2-manifold (here) and at M-theory on G2-manifolds (here)

    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 31st 2017
    • (edited Jul 31st 2017)

    I added the new reference

    Dominic Joyce, Spiro Karigiannis, A new construction of compact G 2G_2-manifolds by gluing families of Eguchi-Hanson spaces, arXiv:1707.09325

    to G2-manifold

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