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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Over half a year later, dialed back the speculation, as discussed at https://nforum.ncatlab.org/discussion/10108/game-theory/
edited classifying topos and added three bits to it. They are each marked with a comment "check the following".
This is in reaction to a discussion Mike and I are having with Richard Williamson by email.
I gave the reference
the following commentary-line:
for historical context see Hitchin 20, Sec. 8
I admit that I only fully grasp this now, that Jaffe-Quinn’s article was in response to Atiyah’s influence on mathematics in whose wake Witten received the Fields medal.
I have tried to brush up the entry dense subcategory a little
(moved the references to the References, moved the part that alluded to the application with nerves to its own section and expanded slightly, added the relevant back-links).
I added to cylinder object a pointer to a reference that goes through the trouble of spelling out the precise proof that for a CW-complex, then the standard cyclinder is again a cell complex (and the inclusion a relative cell complex).
What would be a text that features a graphics which illustrates the simple idea of the proof, visualizing the induction step where we have the cylinder over , then the cells of glued in at top and bottom, then the further -cells glued into all the resulting hollow cylinders? (I’d like to grab such graphics to put it in the entry, too lazy to do it myself. )
<p>I added three more references to <a href="http://ncatlab.org/nlab/show/Bredon+cohomology">Bredon cohomology</a>.</p>
<p>two of them, by H. Honkasolo, discuss a sheaf-cohomology version of Bredon cohomology, realized as the cohomology of a topos built from the <a href="http://ncatlab.org/nlab/show/orbit+category">orbit category</a>.</p>
<p>It's too late for me today now to follow this up in detail, but I thought this might be of interest in the light of our discussion at <a href="http://www.math.ntnu.no/~stacey/Vanilla/nForum/comments.php?DiscussionID=650&page=1">G-equivariant stable homotopy theory</a>.</p>
added references (also to Burnside ring):
Erkki Laitinen, On the Burnside ring and stable cohomotopy of a finite group, Mathematica Scandinavica Vol. 44, No. 1 (August 30, 1979), pp. 37-72 (jstor:24491306, Laitinen79.pdf:file)
Wolfgang Lück, The Burnside Ring and Equivariant Stable Cohomotopy for Infinite Groups (arXiv:math/0504051)
I am slowly creating a bunch of entries on basic concepts of equivariant stable homotopy theory, such as
At the moment I am mostly just indexing Stefan Schwede’s
I am touching various entries related to equivariant stable homotopy theory, adding basics from the literature. For instance I briefly added to G-spectrum the basic definition via indexing on a universe, and added the statement of the equivariant stable Whitehead theorem, cross-linked with the relevant bits at equivariant homotopy theory, etc. I have also been expanding a little more at RO(G)-grading and cross-linked more with old material at equivariant cohomology. Tried to make the link between RO(G)-grading and equivariant suspension isomorphism more explicit.
Just in case you are watching the logs and are wondering. I am not announcing every single edit, unless there is anything noteworthy.
started G-CW complex.
added to orbit category a remark on what the name refers to (since I saw sonebody wondering about that)
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.)
I added a Definition section to Burnside ring (and made Burnside rig redirect to it).
starting something, in equivariant parallel to CW-approximation. Not much here yet, but need to save.
Added alternative terminology “local right adjoint” and “strongly cartesian monad” from Berger-Mellies-Weber. They claim the former “has become the more accepted terminology” than “parametric right adjoint”; does anyone know other references to support this? (I think it’s certainly more logical, in that it fits with the general principle of “local” meaning “on slice categories” — not to be confused with the different general principle of “local” meaning “in hom-objects”.)
There has been a pretty massive expansion at proof net. All who are interested in this are invited to have a look (but the nLab is super-slow in loading now from where I write).
Noam Z., if you are reading this: I had looked at the notes you kindly mentioned to me recently. Could you comment on what the connection might be with the sequentialization result (see the remark 2 under theorem 1 in proof net)? The outline of proof reminded me of your description of inversion and focusing, but I confess I had a little trouble following everything (my fault, not yours).
added to polynomial functor the evident but previously missing remark why it is called a “polynomial”, here.
On occasion of Alexander Schenkel’s most recent talk (here) I am finally splitting off an entry homotopical algebraic quantum field theory from AQFT.
added pointer to:
am slowly starting to add some genuine content to twisted K-theory
have created an entry for Bott periodicity
added to equivariant K-theory comments on the relation to the operator K-theory of crossed product algebras and to the ordinary K-theory of homotopy quotient spaces (Borel constructions). Also added a bunch of references.
(Also finally added references to Green and Julg at Green-Julg theorem).
This all deserves to be prettified further, but I have to quit now.
I fleshed out the page Arf-Kervaire invariant problem, and added a link to the new notes of HHR giving a nice introduction to the problem.
created an entry twisted Umkehr map. The material now has some overlap with what I just put into Pontrjagin-Thom collapse map. But that doesn’t hurt, I think.
added some lines to differential algebraic K-theory
also a stub Beilinson regulator
starting something, to go with and rhyme on equivariant principal bundle. Not done yet, but need to save.
I have created a stub for this at Petri net. I hope to develop the links with higher dimensional automata and also with linear logic.
am giving this its own entry, for ease of hyperlinking.
For the moment this is mostly just the table incarnations of rational equivariant topological K-theory – table adjoined with some basic text around it.
brief category:people
-entry for hyperlinking references at Baum-Connes conjecture
created Baum-Connes conjecture with an emphasis on the Green-Julg theorem (of the statement in KK-theory).
I have started one of those hyperlinked indices at he “reference”-entry K-Theory for Operator Algebras.
I felt we were lacking an entry titled simplicial homotopy theory that usefully collects the relevant entries that we do have. So I am starting one.
I fixed a trivial typo in adjoint functor theorem but left wondering about this:
… the limit
over the comma category (whose objects are pairs and whose morphisms are arrows in making the obvious triangle commute in ) of the projection functor
I don’t really understand this (and while I could figure it out, it’s probably not good to make readers do so). At first it sounds like someone is saying “the limit over the comma category of the projection functor ”, which would be circular. But it must be that both formulas are intended as synonymous definitions of . At that point one is left wondering why one has a backwards arrow under it and the other does not. I guess old-fashioned people prefer writing limits with backwards arrows under them, so someone is trying to cater to all tastes? I think it’s better in this website to use and for limit and colimit.
I could probably guess how to fix this, but I won’t since I might screw something up.
brief category:people
-entry for hyperlinking references at equivariant bundle
started a minimum at writer comonad
brief category:people
-entry for hyperlinking references at G-CW-complex and at equivariant Whitehead theorem, in fact for recording these references:
Takao Matumoto, On -CW complexes and a theorem of JHC Whitehead, J. Fac. Sci. Univ. Tokyo Sect. IA 18, 363-374, 1971
Takao Matumoto, _Equivariant K-theory and Fredholm operators, J. Fac. Sci. Tokyo 18 (1971/72), 109-112 (pdf, MatumotoEquivariantKTheory.pdf:file)
I am not sure if I am correctly identifying webpages related to this author:
The MathsGenealogy page here would plausibly be the correct one – except that it lists a PhD in 1976, while the articles above – which seem to be the author’s main results – are from 1971 !?
brief category:people
-entry for hyperlinking references at equivariant Whitehead theorem
started Elmendorf’s theorem with a brief statement of the theorem
created discrete and codiscrete topology
brief category:people
-entry for hyperlinking references at Elmendorf’s theorem and maybe elsewhere