Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 25th 2019
   • (edited Mar 25th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI want this entry to have an actual section on construction of (compact) Examples, so I started one ([here](https://ncatlab.org/nlab/show/G2+manifold#Examples)). But so far there is nothing in there apart from pointers to the original articles by Joyce and Kovalev, and a graphics illustrating Kovalev's twisted connected sums. <a href="https://ncatlab.org/nlab/revision/diff/G2+manifold/51">diff</a>, <a href="https://ncatlab.org/nlab/revision/G2+manifold/51">v51</a>, <a href="https://ncatlab.org/nlab/show/G2+manifold">current</a>

   I want this entry to have an actual section on construction of (compact) Examples, so I started one (here). But so far there is nothing in there apart from pointers to the original articles by Joyce and Kovalev, and a graphics illustrating Kovalev’s twisted connected sums.

   diff, v51, current

2. • CommentRowNumber2.
   • CommentAuthorAli Caglayan
   • CommentTimeMar 25th 2019
   • (edited Mar 25th 2019)
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexThere are many articles on [Johannes Nordström](http://people.bath.ac.uk/jlpn20/)'s web page. Here is [another article](https://arxiv.org/pdf/1808.09443.pdf) with some more examples. They construct two G2 manifolds which are diffeomorphic but whose G2 structures are not homotopic, hence the title of the article. Mark Haskins is another expert on G2 manifolds, though I can't seem to find his webpage.

   There are many articles on Johannes Nordström’s web page.

   Here is another article with some more examples. They construct two G2 manifolds which are diffeomorphic but whose G2 structures are not homotopic, hence the title of the article.

   Mark Haskins is another expert on G2 manifolds, though I can’t seem to find his webpage.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 25th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexNB, I don't lack articles with examples, what I currently lack is the leisure/energy to extract them into the $n$Lab page.

   NB, I don’t lack articles with examples, what I currently lack is the leisure/energy to extract them into the $n$Lab page.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 14th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded full publication data to * [[Robert Bryant]], _Some remarks on $G_2$-structures_, [Proceedings of the 12th G&#246;kova Geometry-Topology Conference 2005](http://gokovagt.org/proceedings/2005), pp. 75-109 ([arXiv:math/0305124](https://arxiv.org/abs/math/0305124), [webpage](http://gokovagt.org/proceedings/2005/bryant.html), [pdf](http://gokovagt.org/proceedings/2005/ggt05-bryant.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/G2+manifold/54">diff</a>, <a href="https://ncatlab.org/nlab/revision/G2+manifold/54">v54</a>, <a href="https://ncatlab.org/nlab/show/G2+manifold">current</a>

   added full publication data to

   • Robert Bryant, Some remarks on $G_2$-structures, Proceedings of the 12th Gökova Geometry-Topology Conference 2005, pp. 75-109 (arXiv:math/0305124, webpage, pdf)

   diff, v54, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 15th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Dominic Joyce]], _Compact Riemannian manifolds with exceptional holonomy_, Surveys in Differential Geometry Volume 6 (2001) ([doi:10.4310/SDG.2001.v6.n1.a3](https://dx.doi.org/10.4310/SDG.2001.v6.n1.a3)) <a href="https://ncatlab.org/nlab/revision/diff/G2+manifold/55">diff</a>, <a href="https://ncatlab.org/nlab/revision/G2+manifold/55">v55</a>, <a href="https://ncatlab.org/nlab/show/G2+manifold">current</a>

   added pointer to

   • Dominic Joyce, Compact Riemannian manifolds with exceptional holonomy, Surveys in Differential Geometry Volume 6 (2001) (doi:10.4310/SDG.2001.v6.n1.a3)

   diff, v55, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeDec 20th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[Bobby S. Acharya]], Daniel A. Baldwin, *Ricci Flat Metrics, Flat Connections and $G_2$-Manifolds* &lbrack;[arXiv:2312.12311](https://arxiv.org/abs/2312.12311)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/G2+manifold/62">diff</a>, <a href="https://ncatlab.org/nlab/revision/G2+manifold/62">v62</a>, <a href="https://ncatlab.org/nlab/show/G2+manifold">current</a>

   added pointer to today’s

   • Bobby S. Acharya, Daniel A. Baldwin, Ricci Flat Metrics, Flat Connections and $G_2$-Manifolds [arXiv:2312.12311]

   diff, v62, current

7. • CommentRowNumber7.
   • CommentAuthorperezl.alonso
   • CommentTimeFeb 7th 2024
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexpointer to * Marisa Fernández, Luis Ugarte. *Dolbeault Cohomology for $G2$-Manifolds*. Geometriae Dedicata 70, 57–86 (1998). ([doi](https://doi.org/10.1023/A:1004940807017)) <a href="https://ncatlab.org/nlab/revision/diff/G2+manifold/63">diff</a>, <a href="https://ncatlab.org/nlab/revision/G2+manifold/63">v63</a>, <a href="https://ncatlab.org/nlab/show/G2+manifold">current</a>

   pointer to

   • Marisa Fernández, Luis Ugarte. Dolbeault Cohomology for $G2$-Manifolds. Geometriae Dedicata 70, 57–86 (1998). (doi)

   diff, v63, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * Mario Garcia-Fernandez, Jason D. Lotay, Henrique N. Sá Earp, Agnaldo A. da Silva Jr.: *Coupled $G_2$-instantons* &lbrack;[arXiv:2404.12937](https://arxiv.org/abs/2404.12937)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/G2+manifold/71">diff</a>, <a href="https://ncatlab.org/nlab/revision/G2+manifold/71">v71</a>, <a href="https://ncatlab.org/nlab/show/G2+manifold">current</a>

   added pointer to today’s

   • Mario Garcia-Fernandez, Jason D. Lotay, Henrique N. Sá Earp, Agnaldo A. da Silva Jr.: Coupled $G_2$-instantons [arXiv:2404.12937]

   diff, v71, current

9. • CommentRowNumber9.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeJul 17th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexUsed unicode subscripts for indices of [[exceptional Lie groups]] including title and links. When not linked, usual formulas are used. See discussion [here](https://nforum.ncatlab.org/discussion/18215/title-convention). Links will be re-checked after all titles have been changed. (Removed two redirects for "G2 manifold" from the top and added one for "G2 manifold" at the bottom of the page.) <a href="https://ncatlab.org/nlab/revision/diff/G%E2%82%82+manifold/72">diff</a>, <a href="https://ncatlab.org/nlab/revision/G%E2%82%82+manifold/72">v72</a>, <a href="https://ncatlab.org/nlab/show/G%E2%82%82+manifold">current</a>

   Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “G2 manifold” from the top and added one for “G2 manifold” at the bottom of the page.)

   diff, v72, current