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    • I have touched étale groupoid and various entries related to this.

      I have made orbit space redirect to orbit, though eventually it might want to be a separate entry.

      Also I have made foliation theory redirect to folitation, though eventually it might want to be a separate entry.

      I have added Deligne-Mumford stack as a “related concept” to étale groupoid, though eventually what I am after is a complex of entries that discusses approaches to a general notion of étale ∞-groupoids and how these sub-entries fit into a more general story.

      So I’ll be creating a stub étale ∞-groupoid, but I am not sure if I have time and energy to have it be more than a reminder for things to look into later.

    • The relation between slope-(semi-)stability of vector bundles and the general concept of (semi-)stability in the sense of geometric invariant theory seems to be a well-kept secret as far as expositions and lecture notes etc. go. One place where I see a genuine review of this relation is

      • Alfonso Zamora Saiz, On the stability of vector bundles, Master thesis 2009 (pdf)

      I have created an entry

      (with a bunch of variant terms redirecting to it) that is presently just a glorified pointer to the relevant pages in this thesis. Then I have added related comments to the existing entries

    • might anyone have an electronic copy of the English version of Brylinski-Zucker 91 “An overview of recent advances in Hodge theory”?

    • have added to normed field the statement that if the product preserves the norm strictly (by equality, not just by inequality) then one speaks of a “valued field”.

    • I created the page walking structure. I’m open to better names for it. It also probably needs to be linked from a bunch of different places.

    • added to real analytic space the statement and reasoning of Whitneys’s theorem (unformatted for the moment, am in a rush)

    • have added some more references to logarithmic geometry and cross-linked a bit. (but there is still no genuine content)

    • I have deleted a sentence that is not correct. See the last discussion on cellular model category.
      By the way, how do you sign in to nLab. I am signed in to the forum but when I edited it was shown as anonymous coward...
    • I have deleted some sentences that are not correct. See the last discussion on cellular model category.
    • I have deleted some statements that are not correct. It is quite obvious that what I have deleted is wrong, in fact the restatement given a few lines later is the verification of the condition that that map is onto (which is definitely not automatic).

    • started a minimum at analytification, mainly interested for the moment in collecting the references now given there which discuss analytification of algebraic (etc.) stacks

    • I have expanded just a little at KR-theory by giving it an actual Idea-paragraph and adding some more references.

    • I noticed tha tthe entry separable closure existed but was effectively devoid of content. I have now copy-and-pasted the relevant paragraphs from the entry Galois theory into it.

    • I wrote a bit at heap about the empty heap (and its automorphism group, the empty group, which I put in the headline for maximum shock value).

    • Over on MO (in the comments here) Stefan Wendt kindly reminds me of an old nnLab entry I once started on B1-homotopy theory. Have added a reference and hope to be adding more.

    • started Hodge cycle, but my battery is dying right this moment….

    • Larusson formulates the Oka principle homotopy-theoretically as: a complex manifold XX is Oka if for every Stein manifold Σ\Sigma the canonical map

      Maps hol(Σ,X)→Maps top(Σ,X) Maps_{hol}(\Sigma, X) \to Maps_{top}(\Sigma,X)

      between the mapping spaces is a weak homotopy equivalence (see here).

      It is natural to wonder what this looks like in terms of the cohesion of the ∞\infty-topos ℂAnlytic∞Grpd\mathbb{C}Anlytic\infty Grpd over CplxMfdCplxMfd.

      If we write Π:ℂAnlytic∞Grpd→∞Grpd\Pi : \mathbb{C}Anlytic\infty Grpd \to \infty Grpd, then up to possible technicalities to be checked, it should simply mean

      Π[Σ,X]⟶≃[ΠΣ,ΠX] \Pi[\Sigma, X] \stackrel{\simeq}{\longrightarrow} [\Pi \Sigma,\; \Pi X]

      where [−,−][-,-] is the internal hom.

      (Something close to this (but not quite the same) is what Lawvere calls the “axiom of continuity” in a cohesive topos.)

      If instead we work internally and let Π:ℂAnlytic∞Grpd→ℂAnlytic∞Grpd\Pi : \mathbb{C}Anlytic\infty Grpd \to\mathbb{C}Anlytic\infty Grpd be the shape modality, then the above is equivalently

      Π[Σ,X]⟶≃♭[ΠΣ,ΠX]. \Pi[\Sigma, X] \stackrel{\simeq}{\longrightarrow} \flat [\Pi \Sigma,\; \Pi X] \,.

      In either case, it is a very natural condition to ask for in general cohesive ∞\infty-toposes. Maybe one should call it the Oka-Larusson property or something…

    • I split off an entry applications of (higher) category theory from the entry nPOV.

      Hopefully we find the energy to further improve this entry in various ways. For the moment I just added a 1-line intro. And a quote, which I think hits the nail of this entry on the head.

    • added pointers to Fornaess-Stout on complex polydiscs here

    • Somebody emailed me highlighting that the text green here, revision 69 of Dold-Kan correspondence does not quite parse.

      I didn’t write this,though. There is a definition meant to be equivalent to that at combinatorial spectrum, but at least some indices need renamining, and it seems maybe more needs to be fixed or at least added. Not sure. Also I absolutely don’t have the leisure to look into this right now. I hope somebody finds the energy to look into it.

    • created Serre duality with a simple minimum of content

      (I have also briefly touched a bunch of related entries on Dolbeault cohomology etc. but most of them are still in a sad state and need work)

    • I created at equivariant cohomology separate subsections for, so far, Borel equivariant and Bredon equivariant cohomology.

      At Bredon cohomology I added a sentence about the coefficient objects.

    • The nLab entry Spectral Schemes has existed for a long time, now finally the article with that title exists, too. ;-) See the link there

    • only now realized that Zoran had an old entry moduli space of bundles. Have now vigorously cross-linked it with a bunch of related entries

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