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    • Removing the redirect for signal, as I intend to create a page for this shortly.

      diff, v3, current

    • I have added the statement that GG-representation spheres are GG-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.

      diff, v13, current

    • Several popular ways of writing down the tautogical line bundle \mathcal{L} over some projective space don’t generalize, say to the equivariant context.

      This here is better, it seems:

      v (V{0})×k *k × [v,z]([v],vz) V{0}k ××V id×ptk × kP(V) = (V{0})×*k × \array{ \mathcal{L}_v & \coloneqq & \frac{ (V \setminus \{0\}) \times k^\ast }{ k^\times } & \overset{ [v,z] \mapsto \big( [v], v \cdot z \big) }{\hookrightarrow} & \frac{ V \setminus \{0\} }{ k^\times } \times V \\ \big\downarrow && \big\downarrow {}^{\mathrlap{ \frac{id \times pt}{ k^\times } }} \\ k P(V) &=& \frac{ (V \setminus \{0\}) \times \ast }{ k^\times } }

      v1, current

    • I think some editing to the division algebra article is necessary (https://ncatlab.org/nlab/show/division+algebra)

      The approach taken has been presented with a few inconsistencies. It appears to follow John Baez's article (partially) in defining it as a (possibly nonassociative) algebra over a field with no nontrivial zero divisors. This would be fine if the entire article assumed finite dimensionality, but the first paragraph does not, allowing something like R[x] to be termed "a division algebra."

      While I understand the approach in the Baez article is coherent and just fine, I have to question whether or not "no nontrivial zero divisors" is right the way to present division algebras in this context.

      In wikipedia, for example, it's defined just by saying "every element has a two-sided inverse," which Baez calls an algebra "with multiplicative inverses." Baez's definition is apparently strictly weaker.

      I don't know which approach is more historically accurate and/or considered 'the right' approach in current theory.

      I would think that, if not "algebra with multiplicative inverses", then a definition saying that $ax=b$ and $xa=b$ both have unique solutions for any b and any nonzero a, would be the right way to go.
    • Rewriting to prioritize a more standard definition of “division algebra,” while preserving the material and citation to Baez’s less standard version.

      diff, v10, current

    • Page created, but author did not leave any comments.

      v1, current

    • 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 nnLab entry for it does. :-)

    • 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

      • {#Greenlees} John Greenlees, The coefficient ring of equivariant homotopical bordism classifies equivariant formal group laws over Noetherian rings, (preprint, 2001.

      diff, v5, current

    • changing category to algebraic geometry

      Valeria de Paiva

      diff, v8, current

    • removing category: World [private]

      Valeria de Paiva

      diff, v2, current

    • K-cohomology is a strangely organised page with 5 sections identically named. There supposed to be some difference from K-theory

    • Created this page, since references are somewhat hard to find.

      Adrien Brochier

      v1, current

    • I added references to John Baez’s two blog posts on The Geometric McKay Correspondence, Part I, Part II.

      I hadn’t realised the length of legs in the Dynkin diagrams corresponds to the stabilizer order on vertices, edges, faces in the corresponding Platonic solid. So 2,3,5 for E 8E_8 and the icosahedron.

      diff, v5, current

    • added [ISBN 978-3-642-61458-3] (https://www.springer.com/gp/book/9783540610496)

      diff, v5, current

    • 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 ( f\forall_f and f\exists_f 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.

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • starting a bare references-list entry, to be !includeed in the References-sections of relevant entries

      v1, current

    • 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.

      diff, v8, current

    • starting some minimum (this is for Cartan’s map in equivariant de Rham cohomology, maybe the entry deserves an expanded title for disambiguation)

      v1, current

    • 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.

    • a table to collect the various cases of transverse geometries to KK-monopoles, to be !include-ded into the relevant entries

      v1, current

    • 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

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Simply the definition, as found in “Combinatorics of coxeter groups” by Bjorner and Brenti.

      Anonymous

      v1, current

    • 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:

      diff, v9, current

    • some minimum, for completeness of the list at D4

      v1, current

    • This page had, besides its minimum content, somewhat weird formatting overhead. I have deleted that now, including the multiple category:-declarations

      diff, v3, current

    • Added a page about the category FinRel of finite sets and relations, and some of its properties.

      v1, current

    • Added the analogous sheaf condition in terms of covering families

      diff, v20, current