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I have added the statement that -representation spheres are -CW-complexes, with a sketch of the idea of the proof for finite groups (here)
I have been looking for source (be it textbook lecture note or otherwise) that makes this statement and gives a proof in a citable way. But it seems people either like to state it as an exercise or else spell it out only in special cases.
I have created an entry modular equivariant elliptic cohomology.
The subject barely exists, for the moment the entry is to serve two purposes:
first, to highlight that by results of Mahowald-Rezk, Lawson-Naumann, Hill-Lawson this exists as a rather compelling generalization of KR-theory;
second, that the close the relation of KR-theory to type II string theory on orientifolds has previously been conjectured to correspond in the lift of the latter to F-theory to a modular equivariant universal elliptic cohomology.
So while the subject hasn’t been studied yet (it seems), both its construction and plenty of motivation for it already exists. And now also an Lab entry for it does. :-)
added editor names and DOI to:
Added
Greenlees (Greenlees 2001) shows that the equivariant complex cobordism ring classifies equivariant formal group laws over Noetherian rings, but the general conjecture is still open.
and reference
brief category: people
-page for hyperlinking references at equivariant complex oriented cohomology theory
Following this discussion, I have now manually removed the apparently ’generated’ content from Revision 1 of L-theory, to avoid it being associated to Urs’ name.
See also discussion at the Latest Changes page for K-cohomology.
K-cohomology is a strangely organised page with 5 sections identically named. There supposed to be some difference from K-theory
just for completeness, some references at Morse homology
brief category:people
-entry for hyperlinking references at L-complete module
Made a few additions to preimage. Added missing word; added a brief mention of the widely-known general reason for the good preservation-properties of this endofunctor.
The mention of these properties had already been there in preimage, but a reason was still missing. My parenthetical remark should perhaps be expanded and harmonized with existing relevant material on the nLab ( and are already well-documented on some pages), but this requires more care than I can apply to it today. Intend to return to the remark before long.
brief category:people
-entry for hyperlinking references at equivariant K-theory
Adding redirect for Euler’s constant.
touched the first paragraph, making hyperlinked pointers to compact Lie groups, positive energy representations and the Verlinde ring.
Then I replaced “twisted euqivariant K-theoyry” with twisted ad-equivariant K-theory and will give this its own entry now…
have split-off a stub positive energy representation from loop group
added complete referencing of FHT and cross-link with twisted ad-equivariant K-theory
I am filling in more details (definitions, properties) about the various toposes at Models for Smooth Infinitesimal Analysis
added DOI to:
brief category:people
-entry for hyperlinking references at equivariant de Rham cohomology and __equivariant ordinary differential cohomology
I was about to create a new entry “characteristic differential form” when I discrovered this old entry.
Have added more redirects to it and more cross-links with Chern-Weil homomorphism.
I have re-written the content at differentiable manifold, trying to make it look a little nicer. Also gave topological manifold some minimum of content.
I’m interested in editing Mac Lane’s proof of the coherence theorem for monoidal categories, as I recently went through all the gory details myself and wrote it up. I was wondering if anybody has any thoughts on what should be left alone with regard to any future changes. Many people clearly put in a lot of work into the page, but it looks like people got busy and it hasn’t been updated in a while.
I think the first few paragraphs are fine, but I think the rest is a bit wordy, it could be more formal, and notation could be changed (very slightly) to be less clunky. I specifically want to make the current document more formal (e.g., saying “Definition: blah blah”), include some nice diagrams, change the notation (e.g., to avoid using double primes, to avoid denoting a monoidal category as B since I think the letter M pedagogically makes more sense), and complete the incomplete entries at the bottom. I’m not really sure if anyone would be against such changes, hence my inquiry.
brief category: people
-entry for hyperlinking references at equivariant de Rham cohomology
added these pointers:
For analogous discussion see
and for review see
this table used to be hidden at supersymmetry, but it really ought to cross-link its entries. Therefore here its stand-alone version, for !inclusion
added pointer to
Paul Balmer, The spectrum of prime ideals in tensor triangulated categories. J. Reine Angew. Math., 588:149–168, 2005 (arXiv:math/0409360)
Paul Balmer, Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings, Algebr. Geom. Topol., 10(3):1521–1563, 2010 (pdf)
(which have been listed at Paul Balmer all along, but were missing here, strangely)
and to the recent:
starting something, on
brief category: people
-entry for hyperlinking references at equivariant de Rham cohomology
Came across this categorification of pro-object.