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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity 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 infinity integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monads monoid monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages 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 science set set-theory sheaf 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 type type-theory universal variational-calculus

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- Discussion Type
- discussion topicCayley plane
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by David_Corfield
- Last Active 50 minutes ago

I made Cayley plane a little less stubby.

- Discussion Type
- discussion topicspheres -- contents
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 1 hour ago

- Discussion Type
- discussion topicDesargues' theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 hours ago

- Discussion Type
- discussion topicoctonionic projective space
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 hours ago

starting something, for the moment just so as to record that

there is a homeomorphism

$\mathbb{O}P^2 \,\simeq\, S^{15} \underset{h_{\mathbb{O}}}{\cup} \mathbb{H}P_1$between the octonionic projective plane and the attaching space obtained from the octonionic projective line along the octonionic Hopf fibration.

- Discussion Type
- discussion topicHopf invariant
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by David_Corfield
- Last Active 4 hours ago

I have been making trivial edits (adding references, basic statements, cross-links ) to

*Hopf invariant*and a bunch of related entries, such as*Kervaire invariant*,*Hopf invariant one problem*,*Arf-Kervaire invariant problem*,*normed division algebra*.

- Discussion Type
- discussion topic8-sphere
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 hours ago

- Discussion Type
- discussion topicsplit quaternion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 hours ago

- Discussion Type
- discussion topicKonrad Voelkel
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 hours ago

- Discussion Type
- discussion topicprojective G-space
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 7 hours ago

I am giving this its own entry, not to drown it inside

*projective space*

- Discussion Type
- discussion topicIvo Dell'Ambrogio
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 9 hours ago

- Discussion Type
- discussion topicMSp
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by David_Corfield
- Last Active 10 hours ago

have added this pointer:

- Nigel Ray,
*The symplectic bordism ring*, Volume 71, Issue 2 March 1972, pp. 271-282 (doi:10.1017/S0305004100050519)

- Nigel Ray,

- Discussion Type
- discussion topicfactorization lemma
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Urs
- Last Active 10 hours ago

created factorization lemma

- Discussion Type
- discussion topicAdS-QCD correspondence
- Category Latest Changes
- Started by Urs
- Comments 54
- Last comment by Urs
- Last Active 11 hours ago

- Discussion Type
- discussion topicSchwinger effect
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 12 hours ago

- Discussion Type
- discussion topiccobordism theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 23 hours ago

the keyword “cobordism theory” used to redirect to the entry

*cobordism*. While often the latter term is used as shorthand for the former, the entry “cobordism” is really just about the basic notion of cobordisms between manifolds, so redirecting “cobordism theory” to there wasn’t satisfactory.So I gave it an entry in its own right, added a little Idea-section briefly surveying the scope of cobordism theory proper, copied over the relevant references:

Then I included (in that entry directly and into related entry as a “floating table of contents”) a list of pointers to related entries:

- Discussion Type
- discussion topicalgebraic topology
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active 23 hours ago

I have tried to give

*algebraic topology*a better Idea-section.

- Discussion Type
- discussion topiccomplex oriented cohomology theory
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by Urs
- Last Active 1 day ago

added a tiny bit of basics to

*complex oriented cohomology theory*

- Discussion Type
- discussion topicfunctional cup product
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicdiffeological space
- Category Latest Changes
- Started by Urs
- Comments 68
- Last comment by DavidRoberts
- Last Active 1 day ago

seeing Eric create diffeology I became annoyed by the poor state that the entry diffeological space was in. So I spent some minutes expanding and editing it. Still far from perfect, but a step in the right direction, I think.

(One day I should add details on how the various sites in use are equivalent to using CartSp)

- Discussion Type
- discussion topicadjunction between topological spaces and diffeological spaces
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 1 day ago

this is the bare statement of a Proposition, to be

`!include`

-ed into the relevant entries, notably at*diffeological space*and at*Delta-generated topological space*

- Discussion Type
- discussion topicmodel structure on diffeological spaces
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 1 day ago

a stub entry, for the moment just so as to give a home to these two references:

Hiroshi Kihara,

*Model category of diffeological spaces*, Journal of Homotopy and Related Structures, (2018), 1-40 (arXiv:1605.06794)Tadayuki Haraguchi, Kazuhisa Shimakawa,

*A model structure on the category of diffeological spaces*(arXiv:1311.5668)

- Discussion Type
- discussion topicrelation between quasi-categories and simplicial categories
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Guest
- Last Active 1 day ago

one more remark at relation between quasi-categories and simplicial categories

(to be expanded...)

- Discussion Type
- discussion topicHiggs field
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active 1 day ago

added a brief historical comment to

*Higgs field*and added the historical references

- Discussion Type
- discussion topicstuff, structure, property
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by John Baez
- Last Active 1 day ago

I have removed the following discussion box from

*stuff, structure, property*– because the entry text above it no longer contained the word that the discussion is about :-)

[begin forwarded discussion]

+–{: .query} Mike: Maybe you all had this out somewhere that I haven’t read, but in the English I am accustomed to speak, “property” is not a mass noun. So you can “forget a property” or “forget properties” but you can’t “forget property.”

*Toby*: Well, ’property’*can*be a mass noun in English, but not in this sense. Also, if we were to invent an entirely new word for the concept, it would surely be a mass noun. Together, these may explain why it's easy to slip into talking this way, but I agree that it's probably better to use the plural count noun here. =–[end forwarded discussion]

- Discussion Type
- discussion topicVassily Gorbunov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicMichel André
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 2 days ago

- Discussion Type
- discussion topicArunas Liulevicius
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicNigel Ray
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topiccobordism cohomology theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 2 days ago

added pointers on relation of complex cobordism cohomology with divisors, algebraic cycles and Chow groups:

Burt Totaro,

*Torsion algebraic cycles and complex cobordism*, J. Amer. Math. Soc. 10 (1997), 467-493 (doi:10.1090/S0894-0347-97-00232-4)

- Discussion Type
- discussion topicRicci flow
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 2 days ago

added briefly something to Ricci flow, amplifying that it is the gradient flow of the action functional of dilaton gravity (equivalently: the renormalization group flow of the string-sigma-model coupled to gravity and dilaton)