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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I added a link to the published version of my notes on universal simplicial bundles, here on Urs’ web.
brief remark charge conjugation matrix, just because I needed to be able to point to it
added little bit more to super translation Lie algebra, including a remark that it is a central extension of the superpoint, regarded as an abelian super Lie algebra.
started a hyperlinked index for Dan Freed’s Five lectures on supersymmetry
(might use this in a course later this year…)
I only noticed now that the discussion around equation (2.14) in
identifies the exceptional super Lie algebra cocycle on (given by the brane scan) with the “topological membrane” of “topological M-theory”.
I added a brief remark to this extent to topological membrane and updated brane scan accodingly. Hope to be expanding on this soon…
I created a small page for compact symplectic group, which is not the same as the symplectic group, and added some sentences at both to disambiguate. I’m also working on an entry orthogonal group of an inner product space, which will give the general treatment that covers , and (and other cases of mixed signature, like ).
There are interesting charts for using its Lie algebra (in fact various tangent spaces) which don’t come from the exponential mapping, and my aim is to get a reasonably full treatment of these in there.
I added to disjoint subsets.
started an index at Elephant
just a tiny beginning. we have entries for many keywords already.
Added stub for Kontsevich formality.
Also added some comments to the HKR page.
I have added to microcausality a quote with a nice discussion. That also cites experimental bounds. But back from the 1970s only – there must be better ones by now.
Does anyone happen to know a citation for better experimental bounds, or else might anyone enjoy googling for it? I am out of googlin time now, but I am entertaining myself with advertizing this as an “experimental bound on higher category theory in fundamental physics”, along the lines of the story here.
At partition, I've defined partitions of sets, numbers, intervals, measure spaces, and unity on topological spaes, giving these all as special cases of a general concept defined in a monoid whose nonzero elements form an ideal (and possibly equipped with some notion of infinite sum).
for the exposition at motivic quantization (not done yet) I need some keywords being hyperlinked which don’t really have entries yet. So I created some stubs, to be filled with genuine life later, e.g.
and maybe more which I forget. But have to run now. More later.
lightning remark here on Willwacher’s identification of the GT Lie algebra with of the graph complex
New page: split support
I wrote up a brief little note on this on my web. Comments are very welcome. This could be transported to the nLab if one wants.
Added some remarks about Whitehead’s principle as a foundational axiom to Whitehead’s theorem.
surprised that we didn’t have this “people”-entry before, now we do: Kuo Tsai Chen
created amenable topological groupoid. Skipped the definition (gave a pointer, though), just wanted to quickly record that the convolution algebras of amenable groupoids are in the bootstrap category. Added that proposition also there.
Wrote recursive subset and partial recursive function. Not much more than stubs.
created bootstrap category
stub for groupoid K-theory, for the moment just to record some pointers
Created modelizer. It’s not clear to me exactly what Grothendieck is taking as a property or as a structure in his definitions, but I tried to make a guess.
at Witten genus I have tried to give a more complete list of pointers to the story of refining the Witten genus to a map of -ring spectra. Now the references there read as follows:
The refinement of the Witten genus from values in modular forms to topological modular forms and further to a morphism of E-∞ rings, hence to the string orientation of tmf is due to
Michael Hopkins, Topological modular forms, the Witten Genus, and the theorem of the cube, Proceedings of the International Congress of Mathematics, Zürich 1994 (pdf)
Michael Hopkins, Algebraic topology and modular forms, Proceedings of the ICM, Beijing 2002, vol. 1, 283–309 (arXiv:math/0212397)
Matthew Ando, Michael Hopkins, Charles Rezk, Multiplicative orientations of KO-theory and the spectrum of topological modular forms, 2010 (pdf) {#AndoHopkinsRezk}
see also remark 1.4 of
and for more on the sigma-orientation see
Similar additions I have made to topological modula form (which is otherwise an empty entry, alas) and to tmf itself.
An updated version of the book J-holomorphic Curves and Quantum Cohomology can be found on the web page of Dusa McDuff which is linked at the new entry Dusa McDuff ! I also started a stub symplectic topology and just a little longer one for Floer homology.
brief note at category of correspondences on limits and colimits.
Created a new article, countable ordinal.
created Dirac induction with a brief note on the relation to the orbit method, via FHT-II.
I have added
bivariant cohomology theory, in order to record some references
I started a page about the simplicial bar construction. I haven’t checked all the details carefully (especially regarding -naturality!) though.
added a brief remark to discrete object in a new section Examples — in infintiy-toposes on the relation between discreteness and cohomology.
This is a (fairly trivial) comment on Mike’s discussion over on the HoTT blog, linked to from the above.
Lots of changes at motivic cohomology.
The stuff about the homotopy localization of the Nisnevich (∞,1)-topos I will move to A1-homotopy theory where it more properly belongs.
I decided to add some content to the motivic pages here on the nLab.
I started with Nisnevich site. More to come soon…
at compactification I added in the second sentence of the Idea-section a pointer to one-point compactification, to have that mentioned before then the next line starts talking about more general situations.
(prompted by this physics.SE question)
trivia, but I just ran into this:
I noticed we have entries:
and
both of them referring to operator algebraists. First I thought we need to merge these entries. But after looking around I guess these are indeed two different people. (The German Wikipedia claims here that the second initial of the author of K-Theory for Operator Algebras is “E” not “A”).
(Notice that the second entry is mistaken, where it says “Home page” it points not to some author’s home page but to the nLab home page…)
Just making sure. Sorry for the distraction.
I was starting to make some notes on the new article by Sergei Gukov and Anton Kapustin, at a new “reference”-categorized entry titled
Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories
But so far there is just a vague indication of the main thrust. I want to flesh out more detail later. On the other hand, tomorrow morning I’ll be going on a two week vacation, so this plan will encounter delays.
For the sake of illustration I have added to ordinary homology a section In terms of higher linear algebra.
Currently the main point is to record, after some preliminaries, the standard observation plus detailed proof that for a topological space, its ordinary chain complex of singular simplices is, up to equivalence, the -colimit of the tensor unit local system with coefficients in . (Its “-Thom spectrum”.)
In the section compacta as algebras, I have written out complete details of a proof that compact Hausdorff spaces are monadic over sets.
concerning stable map: is there some nice abstract characterization? Something involving maybe the words “faithful functor of étale groupoids”?
Added a section with a little bit of detail on model structures on cochain complexes in non-negative degree to model structure on chain complexes.
localizer, just for completeness
created a minimum at Hermitian structure.
Also edited and expanded the Idea- section at Käher structure a bit.
stub for compact closed 2-category to accomodate a pointer to Mike Stay’s recent article
I am starting an entry Poincaré duality algebra, but it still needs some attention
created unitisation of C*-algebras
stub for chiral ring
(not good yet)
I began to expand Tarski-Seidenberg theorem (formerly a stub) by including some commentary on its significance, and some related results. This is to help create a niche for Schanuel’s conjecture, yet to be written, but which was invoked in a discussion at MO.
stub for metaplectic correction
brief statement of Kodaira vanishing theorem for the complex geometry case
started a stub equivariant KK-theory with some quick notes. But still very stubby.
Wrote a section General weighted colimit formula at homotopy colimit
giving a general formula
spelling out the special case of simplicial diagrams, that reproduces the Bousfield-Kan formula
spelling out the special case of pushout diagrams, that reproduces the formula (or its dual) discussed more in detail in the other examples that were already present
I tried to collect some references at crossed product C*-algebra on their relation to convolution C*-algebras of action groupoids. But I guess I run out of steam…
while writing Baum-Connes conjecture I happened to add some stuff to analytic assembly map.
I have added a new paragraph to direct image about direct image functor with compact support . Eventually I would create a separate entry direct image with compact support, but not yet.
started dual morphism but then began to hesitate: we must have this discussion somewhere already. But where?
Treating locally path-connected spaces as nice topological spaces, we see that nice path-connected spaces are the same as nice connected spaces, and the definition of the latter is more elementary (in point-set topology) than the former. Then nice simply connected spaces are the same as nice unicoherent spaces, which are again more elementary. This should continue for the entire hierarchy of -connected spaces, so I wrote something there about it.
started a table of contents integration theory - contents and added it as a floating TOC to the relevant entries.
(Mostly as a reminder to myself to write more on fiber integration in generalized cohomology…)
Added the following to the references at stable homotopy theory and algebraic topology:
Brief indications of open questions and future directions (as of 2013) of algebraic topology and stable homotopy theory are in
- Tyler Lawson, The future, Talbot lectures 2013 (pdf)
created asymptotic series