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cross-linked with Euler form and added these pointers:
Discussion of Euler forms (differential form-representatives of Euler classes in de Rham cohomology) as Pfaffians of curvature forms:
{#MathaiQuillen86} Varghese Mathai, Daniel Quillen, below (7.3) of Superconnections, Thom classes, and equivariant differential forms, Topology Volume 25, Issue 1, 1986 (10.1016/0040-9383(86)90007-8)
{#Wu05} Siye Wu, Section 2.2 of Mathai-Quillen Formalism, pages 390-399 in Encyclopedia of Mathematical Physics 2006 (arXiv:hep-th/0505003)
Hiro Lee Tanaka, Pfaffians and the Euler class, 2014 (pdf)
{#Nicolaescu18} Liviu Nicolaescu, Section 8.3.2 of Lectures on the Geometry of Manifolds, 2018 (pdf, MO comment)
added to the Properties-section at Hopf algebra a brief remark on their interpretation as 3-vector spaces.
a bare list of bibitems, to be !include-ed into the References-section of relevant entries (such as fractional quantum Hall effect and Laughlin wavefunctions), for ease of synchronization
I started an idea section at transgression, but it could probably use some going over by an expert. I hope I didn’t mess things up too badly. I was reading Urs’ note on “integration without integration” on the train ride home and fooled myself into thinking I understood something.
By the way, this reminded me of a discussion we had a while back
created a brief entry IKKT matrix model to record some references. Cross-linked with string field theory, and with BFSS matrix model
Started this, following this comment.
I wrote a little piece at general covariance on how to formalize the notion in homotopy type theory. Just for completeness, I also ended up writing a little blurb at the beginning about the genera idea of general covariance.
starting an entry on the integer Heisenberg group.
For the moment it remains telegraphic as far as the text is concerned (no Idea-section)
but it contains a slick (I find) computation of the modular transformation of Chern-Simons/WZW states from the manifest modular automorphy of certain integer Heisenberg groups.
Hope to beautify this entry a little more tomorrow (but won’t have much time, being on an intercontinental flight) or else the days after (where I am however at a conference, but we’ll see).
the entry braid group said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).
added to polynomial functor the evident but previously missing remark why it is called a “polynomial”, here.
added publication details for this reference:
and am copying it over to compactly generated topological space, too
I have added to orthogonal factorization system
in the Definition-section three equivalent explicit formulations of the definition;
in the Properties-section the statement of the cancellability property.
Wanted to add more (and to add the proofs). But have to quit now. Maybe later.
I treid to clean up Whitehead tower a bit:
I rewrote and expanded the Idea/Definition part.
Then I moved David Roberts' material that was there to the appropriate section at the new Whitehead tower in an (infinity,1)-topos. (There I tried to add some introductory remarks to it but will try to further highlight David's results here in a moment).
At Whitehead tower I left just a new section that says that there is a notion of Whitehead towers in more general contexts with a pointer to Whitehead tower in an (infinity,1)-topos
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.)
I finally gave the Connes-Lott-Chamseddine-Barrett model its own entry. So far it contains just a minimum of an Idea-section and a minimum of references.
This was prompted by an exposition on PhysicsForums Insights that I wrote: Spectral standard model and String compactifications
tried to polish one-point compactification. I think in the process I actually corrected it, too. Please somebody have a close look.
as mentioned in another thread, I have expanded the Idea-section at polarization in order to highlight the relation to canonical momenta (which I also edited accordingly).
started an Examples-section at geometric quantization
there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).
I have added a remark on this in the -entry here and also at quantum gravity here.
I have been expanding and polishing the entry Heisenberg group.
This had existed in bad shape for quite a while, but now it’s maybe getting into better shape.
I tried to spend some sentences on issues which I find are rarely highlighted appropriately in the literature. So there is discussion now of the fact that
there are different Lie groups for a given Heisenberg Lie algebra,
and the appearance of an “” in may be all understood as not picking the simply conncted ones of these;
I also added remarks on the relation to Poisson brackets, and symplectomorphisms.
In this context: either I am dreaming, or there is a mistake in the Wikipedia entry Poisson bracket - Lie algebra.
There it says that the Poisson bracket is the Lie algebra of the group of symplectomorphisms. But instead, it is the Lie algebra of a central extension of the group of Hamiltonian symplectomorphisms.
I took the liberty of incorporating material from Andre Joyal's latest message to the CatTheory mailing list into the entry dagger-category:
created sections
added to group extension a section on how group extensions are torsors and on how they are deloopings of principal 2-bundles, see group extension – torsors
Initial stub to record some references. Wanted by type theoretic model category
The entry test category which I wrote some time ago, came into the attention of Georges Maltsiniotis who kindly wrote me an email with a kind praise on nlab and noting that his Astérisque treatise on the topic of Grothendieck’s homotopy theory is available online on his web page and that the Cisinski’s volume is sort of a continuation of his Astérisque 301. Georges also suggested that we should emphasise that a big part of the Pursuing Stacks is devoted to the usage of test categories, so I included it into the bibliography and introductory sentence. I hinted to Georges that when unhappy with a state of an nlab entry he could just feel free to edit directly.
Have added to pushout-product the statement (here) that pushout product of -cofibrations with -cofibrations lands in -cofibrations; and (here) the example of pushout products of the inclusions . Both without proof for the moment.