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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 topicspectral sequence of a filtered complex
- Category Latest Changes
- Started by jcmckeown
- Comments 16
- Last comment by Urs
- Last Active Apr 2nd 2019

new entry spectral sequence of a filtered complex, !included into the correct section of spectral sequence. Doubtless still needs tidying.

- Discussion Type
- discussion topicpin group
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 2nd 2019

- Discussion Type
- discussion topiccountably locally finite set of subsets
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 1
- Last comment by Daniel Luckhardt
- Last Active Apr 2nd 2019

Created page on this property in connection with Nagata-Smirnov metrization theorem.

- Discussion Type
- discussion topicNagata-Smirnov metrization theorem
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 1
- Last comment by Daniel Luckhardt
- Last Active Apr 2nd 2019

- Discussion Type
- discussion topicF-theory
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Apr 2nd 2019

started an entry

*F-theory*(the string-theoretic notion)

- Discussion Type
- discussion topicproper map
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Apr 2nd 2019

For better readability, I have split off

*proper map*(topology) from*proper morphism*(general) and added disambiguation. Added classes of examples at*proper map*.

- Discussion Type
- discussion topicseparable space
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by Daniel Luckhardt
- Last Active Apr 1st 2019

I added some more material and references to separable space. Partly this was just to record a MO discussion which would otherwise get eventually buried under centuries of MO sediment, but I’ve included some other things as well. (E.g., I wasn’t aware until now that a product of

*continuum many*separable spaces was still separable.)

- Discussion Type
- discussion topicKan extension
- Category Latest Changes
- Started by Mike Shulman
- Comments 48
- Last comment by nLab edit announcer
- Last Active Apr 1st 2019

I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?

- Discussion Type
- discussion topicmaximal subgroup
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by RodMcGuire
- Last Active Apr 1st 2019

- Discussion Type
- discussion topicflabby sheaf
- Category Latest Changes
- Started by IngoBlechschmidt
- Comments 14
- Last comment by jonsterling
- Last Active Apr 1st 2019

Added to

*flabby sheaf*several characterizations of flabbiness, an external one which, unlike the usual definition, is manifestly local, and several internal ones.

- Discussion Type
- discussion topicSO(3)
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Apr 1st 2019

- Discussion Type
- discussion topicRoger Godement
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Urs
- Last Active Apr 1st 2019

Wrote up a quick article on Roger Godement.

- Discussion Type
- discussion topicbicategory
- Category Latest Changes
- Started by Ahmed
- Comments 2
- Last comment by Urs
- Last Active Apr 1st 2019

- Discussion Type
- discussion topicLie group
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Apr 1st 2019

tried to bring the entry Lie group a bit into shape: added plenty of sections and cross links to other nLab material. But there is still much that deserves to be done.

- Discussion Type
- discussion topicequivariant K-theory
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by nLab edit announcer
- Last Active Mar 31st 2019

added to

*equivariant K-theory*comments on the relation to the operator K-theory of crossed product algebras and to the ordinary K-theory of homotopy quotient spaces (Borel constructions). Also added a bunch of references.(Also finally added references to Green and Julg at

*Green-Julg theorem*).This all deserves to be prettified further, but I have to quit now.

- Discussion Type
- discussion topicFerdinand Veldkamp
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2019

- Discussion Type
- discussion topicTonny Springer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2019

- Discussion Type
- discussion topictriality
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 31st 2019

- Discussion Type
- discussion topicmaximal compact subgroup
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Mar 31st 2019

I have tried to start a table at

*maximal compact subgroup*listing Lie groups and their max compact subgroups. But once again the table does not want to typeset properly.Have to run now, will try to fiddle with this later.

- Discussion Type
- discussion topicoctonionic Hopf fibration
- Category Latest Changes
- Started by David_Corfield
- Comments 25
- Last comment by Urs
- Last Active Mar 31st 2019

Since there wasn’t a page octonionic Hopf fibration, I started one, copying over the start of quaternionic Hopf fibration. The weirdness of the octonions doesn’t prevent anything there, does it?

- Discussion Type
- discussion topicquaternionic Hopf fibration
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 31st 2019

I have created an entry on the

$[\Sigma^\infty_G S^7 , \Sigma^\infty_G S^4]_G \simeq \mathbb{Z} \oplus \cdots$*quaternionic Hopf fibration*and then I have tried to spell out the argument, suggested to me by Charles Rezk on MO, that in $G$-equivariant stable homotopy theory it represents a non-torsion element infor $G$ a finite and non-cyclic subgroup of $SO(3)$, and $SO(3)$ acting on the quaternionic Hopf fibration via automorphisms of the quaternions.

I have tried to make a rigorous and self-contained argument here by appeal to Greenlees-May decomposition and to tom Dieck splitting. But check.

- Discussion Type
- discussion topicSpin(9)
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2019

- Discussion Type
- discussion topicNarain group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active Mar 30th 2019

added pointer to

- Hirosi Ooguri, Zheng Yin,
*TASI Lectures on Perturbative String Theories*(arXiv:hep-th/9612254)

But I was really looking for a solid reference for the basic statement that the maximal compact subgroup of $O(n,n)$ is $O(n) \times O(n)$.

- Hirosi Ooguri, Zheng Yin,

- Discussion Type
- discussion topicbitopological space
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 4
- Last comment by Daniel Luckhardt
- Last Active Mar 30th 2019

- Discussion Type
- discussion topicSpin(8)-subgroups and reductions -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2019

- Discussion Type
- discussion topicJames Sparks
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2019

brief

`category:people`

-entry for hyperlinking references at

- Discussion Type
- discussion topicSU(2)-structure
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 30th 2019

- Discussion Type
- discussion topic5-manifold
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 30th 2019

a bare minimum, for the moment just so as to record this references:

- {#CadekVanzura93} Martin Čadek, Jiří Vanžura,
*On the classification of oriented vector bundles over 5-complexes*, Czechoslovak Mathematical Journal, Vol. 43 (1993), No. 4, 753–764 (dml:128427)

- {#CadekVanzura93} Martin Čadek, Jiří Vanžura,

- Discussion Type
- discussion topicgeneralized Spin(7)-manifold
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2019

- Discussion Type
- discussion topicInitiality Project - Participants
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by raghu
- Last Active Mar 30th 2019

Moved from main Initiality Project page.