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

• created page, more to come

• Hello. There is possible confusion between the notions of separated set and separated subset, which have different pages and mean different things. Any advice on how to handle this?

Thanks!

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

• Created page, to be renamed to “stably compact space”, more to come.

• I added few words about the derived background behind the Duflo map (all comes from a deep insight of Kontsevich, later detailed by many authors).

• Dev Sinha, Section 1 in: Koszul duality in algebraic topology - an historical perspective, J. Homotopy Relat. Struct. (2013) 8: 1 (arXiv:1001.2032)
• am finally splitting this off from Hopf degree theorem, to make the material easier to navigate. Still much room to improve this entry further (add an actual Idea-statement to the Idea-section, add more examples, etc.)

• Unfortunately, I need to discuss with you another terminological problem. I am lightly doing a circle of entries related to combinatorial aspects of representation theory. I stumbled accross permutation representation entry. It says that the permutation representation is the representation in category $Set$. Well, nice but not that standard among representation theorists themselves. Over there one takes such a thing – representation by permutations of a finite group $G$ on a set $X$, and looks what happens in the vector space of functions into a field $K$. As we know, for a group element $g$ the definition is, $(g f)(x) = f(g^{-1} x)$, for $f: X\to K$ is the way to induce a representation on the function space $K^X$. The latter representation is called the permutation representation in the standard representation theory books like in

• Claudio Procesi, Lie groups, an approach through invariants and representations, Universitext, Springer 2006, gBooks

I know what to do approximately, we should probably keep both notions in the entry (and be careful when refering to this page – do we mean representation by permutations, what is current content or permutation representation in the rep. theory on vector spaces sense). But maybe people (Todd?) have some experience with this terminology.

Edit: new (related) entries for Claudio Procesi and Arun Ram.

• tried to polish one-point compactification. I think in the process I actually corrected it, too. Please somebody have a close look.

• Andrea Fontanella, Tomas Ortin, On the supersymmetric solutions of the Heterotic Superstring effective action (arxiv:1910.08496)
• started a bare minimum at Poisson-Lie T-duality, for the moment just so as to have a place to record the two original references

• For now created page, more to be added soon.

• A student asked “What is a cobordism?” and I checked and realized that the $n$Lab entry cobordism was effectively empty.

So I have now added some basic text in the Idea-section and added a bare minimum of references. Much more should be done of course, but at least now there are pointers.

• At the old entry cohomotopy used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.

(We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

• changed “an English mathematician of Egyptian origin” to “a British-Lebanese mathematician”.

In checking his “origin” on Wikipedia…

…I see that Wikipedia says that Sir Michael Atiyah has died. Today.

(!?)

• Added a reference of Robert Furber, Bart Jacobs at Giry monad.

• a small contents entry, to be !include-ed into relevant entries, for ease of hyperlinking

• added to the Idea-section (here) the description of PT-collapse as the function that assigns “asymptotic distance form the submanifold”, an illustrating graphics, and a comment that this represents the Cohomotopy charge of the submanifold

• starting something

• a stub, as requested here

• Created page, more to come.

• I am starting a page about the pentagon relation for multiplicative unitaries and related mathematics. The page for pentagon relation should be a separate page, as one does not really need the real forms and unitarity condition for the pentagon to work; this pentagon relations is sometimes called pentagon equation. $n$Lan uses pentagon equation as a redirect to pentagon identity from the axioms of (coherent) monoidal category, which is usually called pentagon identity indeed, and the terms relations and equation are more used in the context of dilogarithms, quantum groups, operator algebras and alike subjects, all related. The pentagon coherence is in fact related to all of these in a large subset of cases which can be directly expressed categorically, but the literature is quite different in flavour and eventually I will build 3 different pages with redirects and other superstructure, and references to the related terms like Drinfeld associator.

• I added few references, e.g. on the logarithmic CFT case. Maybe the entry should be fused with fusion ring, I see no reason to discuss it separately, the entries are both sketchy and have little material so far.