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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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.
Made a start on taut functor. Mike, I mentioned your work with Cruttwell on generalized multicategories in a section on applications.
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.
stub for iterated integral (more references as soon as the nLab wakes up again…)
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
Someone started a page called probability amplitudes but with a single word. I have changed that to say the page is empty. (which of course it is not!) as I did not feel competent to write even a stub on that topic.
created models in presheaf toposes with the statement of the fact that T-models in presheaves are presheaves of T-models, at least for T a geometric theory.
Added a pointer to this from the corresponding discussion at group object.
I made a stub uniform convergence space, but I need to read the reference.
created a table holographic principle – table (meant to show at on glance what the dictionaty is) and included it into the relevant entries.
stub for perfect complex
I have added to Knizhnik-Zamolodchikov connection
a new paragraph in the Idea section: Idea – From geometric quantization of Chern-Simons theory
a bunch of commented references
There was some misnumbering (sometimes off by 1, sometimes reversed) at homotopy group#truncconn, which hopefully I've fixed.
added to odd line a brief remark on the nature of its automorphism super-group and the consequences, also added some relevant references.
(I feel like I had added this statement to the Lab elsewhere already long time ago, but can’t find it now.)
I was fixing some Spam at generator and noticed that Grothendieck category has a link to generator, but shouldn’t this be to separator? I have fixed it so that the term generator in Grothendieck category links to separator.
I tried to clear up some formatting problems / typos at separator. (There is a query near the bottom of the page that seems to still be unanswered.) Can someone glance at the entry to check my reformatting is right as I was on autopilot when doing it!
A short note at denial inequality, since the subject came up. Mike, please check that I used ‘disequality’ correctly.