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2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck 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 kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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 simplicial space spin-geometry stable-homotopy-theory stack string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicM-theory on G2-manifolds
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Mar 25th 2019

started

*M-theory on G2-manifolds*

- Discussion Type
- discussion topichomology sphere
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2019

- Discussion Type
- discussion topicconjugate subgroup
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2019

am finally giving this its own entry, for ease of hyperlinking. (Many entries point to conjugation action when talking about conjugacy classes of subgroups. Eventually they should be made to point here.)

- Discussion Type
- discussion topicPatrick Koppenburg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2019

brief

`category:people`

-entry for hyperlinking references at*flavour anomaly*and*LHCb*

- Discussion Type
- discussion topicdifferential string structure
- Category Latest Changes
- Started by Urs
- Comments 40
- Last comment by DavidRoberts
- Last Active Mar 24th 2019

am starting differential string structure, but not much there yet

- Discussion Type
- discussion topicArf-Kervaire invariant problem
- Category Latest Changes
- Started by DavidRoberts
- Comments 6
- Last comment by Alizter
- Last Active Mar 24th 2019

I fleshed out the page Arf-Kervaire invariant problem, and added a link to the new notes of HHR giving a nice introduction to the problem.

- Discussion Type
- discussion topicChoice operator
- Category Latest Changes
- Started by Harry Gindi
- Comments 6
- Last comment by nLab edit announcer
- Last Active Mar 24th 2019

- I added a little discussion of Bourbaki's formalism using the global choice operator choice operator.

- Discussion Type
- discussion topicI8
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 24th 2019

- Discussion Type
- discussion topica priori knowledge physics
- Category Latest Changes
- Started by aleksr
- Comments 18
- Last comment by Mike Shulman
- Last Active Mar 24th 2019

- Discussion Type
- discussion topicNicolas Tabareau
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Mar 24th 2019

- Discussion Type
- discussion topicAusdehnungslehre
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 24th 2019

- Discussion Type
- discussion topicAndreas Wipf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 24th 2019

- Discussion Type
- discussion topicBerezin integral
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 24th 2019

- Discussion Type
- discussion topicexotic 7-sphere
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 24th 2019

am splitting off this entry from

*exotic smooth strcuture*, in order to facilitate linking to specifically the case of exotic 7-sphere.Accordingly, so far the bulk of the entry is just copied over from the corresponding section at

*exotic smooth structure*,But I also added a new paragraph,

and that is what motivated me to split this off. Namely it occured to me that from the point of view of M-theory on 8-manifolds, Milnor’s classical construction of exotic smooth 7-spheres as boundaries of 8-manifolds is very particularly the construction of near horizon limits of black M2-brane spacetimes in the context of M-theory on 8-manifolds.

This must be known in the literature, and I’d like to collect what is known about it. So far I found a brief comment in this direction, in section 3.2 of

- David Morrison, M. Ronen Plesser, section 3.2 of
*Non-Spherical Horizons, I*, Adv.Theor.Math.Phys.3:1-81, 1999 (arXiv:hep-th/9810201)

Will be adding more as I find more.

- David Morrison, M. Ronen Plesser, section 3.2 of

- Discussion Type
- discussion topicM. Ronen Plesser
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 24th 2019

brief

`category:people`

-entry for hyperlinking references at*8-manifold*,*M-theory on 8-manifolds*and*exotic 7-sphere*

- Discussion Type
- discussion topichyperanalytic function
- Category Latest Changes
- Started by aleksr
- Comments 3
- Last comment by Richard Williamson
- Last Active Mar 23rd 2019

This is a base topic of my contribution. It introduces a new function that gives series whose coefficients are powers of fine structure constant. Furthermore each member represents natural physical interaction. It can be treated as natural physics that introduces natural particles.

May be I made a lot of mistakes. I will correct them.

- Discussion Type
- discussion topiclinear logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by BenMacAdam
- Last Active Mar 23rd 2019

The cut rule for linear logic used to be stated as

If $\Gamma \vdash A$ and $A \vdash \Delta$, then $\Gamma \vdash \Delta$.

I don’t think this is general enough, so I corrected it to

If $\Gamma \vdash A, \Phi$ and $\Psi,A \vdash \Delta$, then $\Psi,\Gamma \vdash \Delta,\Phi$.

- Discussion Type
- discussion topicEuler characteristic
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 23rd 2019

In order to accompany the nCafe discussion I have started to add some content to the entry Euler characteristic

- Discussion Type
- discussion topicPoincaré–Hopf theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 23rd 2019

- Discussion Type
- discussion topic8-manifold
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 23rd 2019

- Discussion Type
- discussion topicsignature genus
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 23rd 2019

I may have written something at

*signature genus*, but it is at best a stub for the moment

- Discussion Type
- discussion topicstandard model of cosmology
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 23rd 2019

added this, under References – Review:

- V.F. Mukhanov,
*Quantum Universe*, Phys.Usp. 59 (2016) no.10, 1021-1027 (spire:1507528, doi:10.3367/UFNe.2016.07.037857)

In March 2013, following an accurate processing of available measurement data, the Planck Scientific Collaboration published the highest-resolution photograph ever of the early Universe when it was only a few hundred thousand years old. The photograph showed galactic seeds in sufficient detail to test some nontrivial theoretical predictions made more than thirty years ago. Most amazing was that all predictions were confirmed to be remarkably accurate. With no exaggeration, we may consider it established experimentally that quantum physics, which is normally assumed to be relevant on the atomic and subatomic scale, also works on the scale of the entire Universe, determining its structure with all its galaxies, stars, and planets.

- V.F. Mukhanov,

- Discussion Type
- discussion topiclow-dimensional topology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 23rd 2019

included and cross-linked with the tables

- Discussion Type
- discussion topiclow dimensional manifolds -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 23rd 2019

- Discussion Type
- discussion topicBen Allanach
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 23rd 2019

brief

`category:people`

-entry for hyperlinking references at*flavour anomaly*

- Discussion Type
- discussion topicaccessible category
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Mike Shulman
- Last Active Mar 22nd 2019

quickly added at accessible category parts of the MO discussion here. Since Mike participated there, I am hoping he could add more, if necessary.

- Discussion Type
- discussion topicSpin(4)
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 22nd 2019

- Discussion Type
- discussion topicJiří Vanžura
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 22nd 2019

brief

`category:people`

-entry for hyperlinking references at*quaternion-Kähler manifold*,*quaternion-Kähler manifold*and elsewhere

- Discussion Type
- discussion topicArthur Besse
- Category Latest Changes
- Started by James Francese
- Comments 4
- Last comment by James Francese
- Last Active Mar 22nd 2019

- Discussion Type
- discussion topiclow dimensional rotation groups -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 22nd 2019