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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 14th 2012
   • (edited Dec 14th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexexpanded 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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 4th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a brief remark on _[weak G2 holonomy](http://ncatlab.org/nlab/show/G2+manifold#WeakG2Holonomy)_. Needs to be expanded...

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

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 12th 2015
   • (edited Jan 12th 2015)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have expanded a little at _[G2-structure](http://ncatlab.org/nlab/show/G2+manifold#G2Structure)_, added the characterization via "definite" 3-forms, such as to then add a brief section on _[closed G2-structure](http://ncatlab.org/nlab/show/G2+manifold#ClosedG2Structure)_ -- all following the nice note [Bryant 05](http://ncatlab.org/nlab/show/G2+manifold#Bryant05). The upshot is a [remark](http://ncatlab.org/nlab/show/G2+manifold#AtlasForClosedG2tructureInTermsOfHigherGeometry) that closed $G_2$-structures are given by certain phased correspondences of cohesive homotopy types.

   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.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 17th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to [[G2-manifold]] as an [example](http://ncatlab.org/nlab/show/G2+manifold#DefiniteFormsInTermsOfVielbeinFields) discussion of how the "definite" 3-forms are given by contraction of the canonical one with vielbein fields.

   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.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 6th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexjust 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.

   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.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 4th 2015
   • (edited Dec 4th 2015)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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](http://ncatlab.org/nlab/show/G2+manifold#G2manifold).

   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.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2017
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   Author: Urs
   Format: MarkdownItexonly 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](https://ncatlab.org/nlab/show/G2+manifold#Kovalev00)) and at _[[M-theory on G2-manifolds]]_ ([here](https://ncatlab.org/nlab/show/M-theory+on+G2-manifolds#GHKY17))

   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)

8. • CommentRowNumber8.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 1st 2017
   • (edited Aug 1st 2017)
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   Author: DavidRoberts
   Format: MarkdownItexI 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](https://arxiv.org/abs/1707.09325) to [[G2-manifold]]

   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