I added the new reference

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

to G2-manifold

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

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 $G_2$-structures (hence $G_2$-manifold structures) are precisely the torsion-free $G_2$-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.

]]>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.

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.

]]>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 $G_2$-structures are given by certain phased correspondences of cohesive homotopy types.

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

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.