An article

- Fabio Apruzzi, Federico Bonetti, Iñaki García Etxebarria, Saghar S. Hosseini, Sakura Schafer-Nameki,
*Symmetry TFTs from String Theory*(arXiv:2112.02092)

referencing Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds

]]>More subtle questions require working on some generalised differential cohomology theory, of which there are many types. The generalised cohomology theory appropriate for M-theory has been postulated in [68]. It would be interesting to see if this more refined picture leads to any interesting consequences in field theory.

Ah, thanks, that was a bad oversight. Fixed now.

]]>This situation of twisted differential cohomology of curved spacetimes can of course be discussed, too (cite character article)

Missing citation

]]>Thanks, right. Fixed now. Have also improved the figure of the stereographic projection.

]]>Remark 2.2(a)

3-spheres $S^7$

2.2(e)

Finally, while flat Minkowski spacetimes themselves are homotopically trivial, it is this constraint that charges vanishing at infinity which makes them appear to their charge cohomology theory as effective spheres with non-trivial topology

is ungrammatical. ’Vanish’ rather than ’vanishing’?

to understand the n-sphere as being but the homeomorphism type…

’but’ in the sense of ’merely’ or ’simply’ sounds rather old-fashioned/poetic to my ear.

]]>A referee of “M/F-Theory as $M f$-theory” asked why there are no tangential twists considered in this article, even though the domains seem to be spheres. So we have now added some review and amplification of the nature of compactly supported charge cohomology on pages 6-8 of a revised pdf linked here.

]]>Thanks! Fixed now (here).

]]>]]>equivarint

Some typos in ’The character map in equivariant twistorial Cohomotopy’

]]>advencements; eqivariant (5 occasions)

Right, I agreed to give a 30 min “pre-talk”, which is what starts at 13:30. That’s why in total there will be $\sim$ 90 min.

]]>They have it advertised as 14-15 UK time on their site. But the Zoom session begins at 13.30, right?

I guess advertising is an internal affair.

]]>Disregarding overlay, cover/toc slides and the multitude of skipped slides (you need to follow the links to see the flow of the talk through the file), there are actually no more than 20 slides to be shown in all of parts 0-II.

Thanks for catching the typo. Fixed now.

]]>A brisk pace for 90 minutes.

Since I happened to land on slide 76, there should be $\pi_k(S^4)$ rather than $\pi_k(S^k)$.

]]>For what it’s worth, there is now a first version of slides for a 90 min talk this Thursday at QMU London, with focus, in the second part, on the chord diagrammatics of quantum $\mathrm{D}6\perp \mathrm{D}8$-states, under Hypothesis H.

]]>If we are talking, as we are, about *anni domini*, then the traditional notation is Roman numerals and the proper name for geometry happening from the year 2000 = MM on would be *MM-geometry*.

;-)

]]>A small suggestion: instead of “$21^{st}$ geometry”, I think “$21^{st}$C geometry” will fit.

]]>Thanks for fixing my French!

Regarding $PU(\mathcal{H})$; while this angle is somewhat orthogonal to the intention in the slides, let’s think about it:

At face value, there seem to be only two known $K(\mathbb{Z},n)$-s which are topological groups related to quantum physics, aren’t there. Not counting in $K(\mathbb{Z},0)$, there is the evident $U(1)$ and then all the mystery, if there is such, about $PU(\mathcal{H}) \simeq K(\mathbb{Z},2)$, is contained in Kuiper’s theorem.

Now two examples is really not yet a pattern, in particular if they are so closely two aspects of the same thing.

But back in the days, André Henriques used to claim to have found the next examples in the list, from 2d CFT in AQFT guise. But in the comments below his MO:a/46634 he says (as of Oct. 2017) that the proof remains open (you may have to click on “see more comments”).

I was searching for that old MO discussion just recently, since the theorem about equivariant classifying spaces that we are about to publish (in a matter of weeks, hopefully) makes me want to have more examples of “natural” topological groups whose homotopy type is an EM-space.

If anyone has any news about André’s old idea, or something similar, let me know. Would be great if it worked.

]]>Slide 20, it’s ’né’ for a male.

Slide 23:

But

whycoefficients like $P U_{\omega}$?

I recall John Baez wondering:

]]>For some mysterious reason, it looks like K(Z,n)’s are important quantum physics! This is especially interesting because the abstract definition of the K(Z,n)’s has nothing to do with the complex numbers - just the integers. The complex numbers show up on their own accord. So maybe this hints at some explanation of why the complex numbers are important in quantum mechanics.

Why are K(Z,n)’s connected to quantum theory? I don’t really know. But we can get some clues by asking some more specific questions.

Now I have some slides to show, for tomorrow: here.

]]>They seem to have omitted you from the participant list.

]]>It seems to be drifting to both being acceptable. I was taught ’under way’ as a predicate adjective, e.g., ’the conference is under way’, but usage changes.

]]>Thanks, I have fixed the century now.

I did check with Google for “under way” and its first (or rather 0th) hit offers both versions but then gives two examples which both use the version with a single word. Now scrolling further down I see the point is the subject of some discussion. But also it looks like Google is messing this up with whitespace, as it claims that “people also ask” the question “Is it underway or underway?” :-)

]]>It does fit very nicely with Friedman’s schema of the need for a new geometry.

Typos:

With the 21st centrury now well underway,

’century’ and ’under way’, usually two words as an adverb

]]>For what it’s worth, I have bee experimenting with producing title and abstract for the next (second) installment of: “String and M-Theory: The New Geometry of the 21st Century – II” via NUS Singapore in Dec 2021.

A first version is now here.

]]>