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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• am adding references, such as this one:

• Francesco Biagazzi, A. l. Cotrone, Holography and the quark-gluon plasma, AIP Conference Proceedings 1492, 307 (2012) (doi:10.1063/1.4763537, slides pdf)
• added a paragraph and a reference to cup product, archiving the blog comment here

• added references by Pronk-Scull and by Schwede, and wrote an Idea-section that tries to highlight the expected relation to global equivariant homotopy theory. Right now it reads like so:

On general grounds, since orbifolds $\mathcal{G}$ are special cases of stacks, there is an evident definition of cohomology of orbifolds, given by forming (stable) homotopy groups of derived hom-spaces

$H^\bullet(\mathcal{G}, E) \;\coloneqq\; \pi_\bullet \mathbf{H}( \mathcal{G}, E )$

into any desired coefficient ∞-stack (or sheaf of spectra) $E$.

More specifically, often one is interested in viewing orbifold cohomology as a variant of Bredon equivariant cohomology, based on the idea that the cohomology of a global homotopy quotient orbifold

$\mathcal{G} \;\simeq\; X \sslash G \phantom{AAAA} (1)$

for a given $G$-action on some manifold $X$, should coincide with the $G$-equivariant cohomology of $X$. However, such an identification (1) is not unique: For $G \subset K$ any closed subgroup, we have

$X \sslash G \;\simeq\; \big( X \times_G K\big) \sslash K \,.$

This means that if one is to regard orbifold cohomology as a variant of equivariant cohomology, then one needs to work “globally” in terms of global equivariant homotopy theory, where one considers equivariance with respect to “all compact Lie groups at once”, in a suitable sense.

Concretely, in global equivariant homotopy theory the plain orbit category $Orb_G$ of $G$-equivariant Bredon cohomology is replaced by the global orbit category $Orb_{glb}$ whose objects are the delooping stacks $\mathbf{B}G \coloneqq \ast\sslash G$, and then any orbifold $\mathcal{G}$ becomes an (∞,1)-presheaf $y \mathcal{G}$ over $Orb_{glb}$ by the evident “external Yoneda embedding

$y \mathcal{G} \;\coloneqq\; \mathbf{H}( \mathbf{B}G, \mathcal{G} ) \,.$

More generally, this makes sense for $\mathcal{G}$ any orbispace. In fact, as a construction of an (∞,1)-presheaf on $Orb_{glb}$ it makes sense for $\mathcal{G}$ any ∞-stack, but supposedly precisely if $\mathcal{G}$ is an orbispace among all ∞-stacks does the cohomology of $y \mathcal{G}$ in the sense of global equivariant homotopy theory coincide the cohomology of $\mathcal{G}$ in the intended sense of ∞-stacks, in particular reproducing the intended sense of orbifold cohomology.

At least for topological orbifolds this is indicated in (Schwede 17, Introduction, Schwede 18, p. ix-x, see also Pronk-Scull 07)

• Is the equivariant suspension spectrum functor still strong monoidal, homotopically?

• some minimum

• stub entry, for the moment just so as to satisfy links

• stub entry, for the moment just so as to satisfy links

• As far as I can tell, Ehrhard’s definition of comprehension requires not just that the fibers have terminal objects but that these are preserved by the reindexing functors. This is automatic if the fibration is a bifibration, as in Lawvere’s version; it’s fairly explicit in Ehrhard’s formulation, and somewhat implicit in Jacobs’ but I believe still present (his “terminal object functor” must, I think, be a fibered terminal object).

• brief category:people-entry for hyperlinking references at quark, lepton and elsewhere

• Page created, but author did not leave any comments.

• added some text and some references

• brief category:people-entry for hyperlinking references at quark and at QCD

• Added the full statement of the theorem.

Anonymous

• added to identity type a mentioning of the alternative definition in terms of inductive types (paths).

• Someone forgot to add an obviously intended diagram

Anonymous

• Fixed the existential quantifier in dictionary

anqurvanillapy

• added a brief historical comment to Higgs field and added the historical references

• added also the complementary cartoon for D-branes in string perturbation theory (the usual picture)

• Just noticed that when this page is shown in a Google search, the link from the Google page does not work. It seems that the “+” sign that used to be in the entry title gets interpreted as a whitespace.

Therefore I am now changing the page name, replacing “+” by “and”. This should fix the problem, once Google picks up the change.

• This page is dedicated to the Stieltjes integral. It is basically a generalization of integrals with respect to a function of bounded variation.

This page will present the main propperties of the Stieltjes integral and show its links with measure theory and other types of integral, mainly the Riemann integral, the Lebesguye integral and the Stieltjes integral.

• I thought it better to use $pred(n)$ rather than $n -1$ in the addition, since it’s supposed to apply to $\infty$.