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I want to collect, for expositional purpose, in one place all the ingredients that go into the story of geometric quantization of the 2-sphere, a simple and archetypical example of geometric quantization.
So far I have included everything (I think) pertaining to the prequantum line bundles, the polarization and the spaces of quantum states. Next I’ll add discussion of the angular momentum quantum operators.
A stub created for smart contracts, primarily focus on the blockchain realization of the idea, with link to the wikipedia and smart contract (zoranskoda).
am giving this statement its own page, for ease of linking from various other entries, such as Burnside ring, equivariant stable cohomotopy, Segal-Carlsson completion theorem
stub for model structure on algebraic fibrant objects
just the bare minimum for the moment, no time...
some trivia here, just for completeness, to go along with entries such as SO(2), Pin(2) etc. and for useful hyperlinking in particular from finite subgroups of SU(2)
brief category:people-entry for hyperlinking references at equivariant cohomotopy
Because of the algebraic Kan complex entry I had a look at the simplicial T-complex page. I am not sure that the current page is quite right in its wording. It is a bit the age old problem of structure or properties. In the algebraic Kan complex, the filler choice function is part of the structure. In a T-complex the thin elements form part of the structure but then properties of the thin elements show that there is a unique choice function taking thin values. They then satisfy some equational conditions.
My thought would be that there should be a bit more precision on the differences between them. For instance I think it is true (but I would need to prove it in detail) that any simplicial T-complex gave an algebraic Kan complex, yielding an ’inclusion functor’ from SimpT to Alg Kan. That functor should have a left adjoint which kills off the Whitehead products etc, (that need not be trivial for an algebraic Kan complex but are for a simplicial T-complex). I do not see how to construct this explicitly but am sure there must be a simple way of imposing conditions on an alg. Kan complex and looking at ’varieties’ in that category. (I have not read Thomas’s thesis and he may have done something related to this already.) In other words, can one impose equations on alg. Kan complexes, in this way. The present definition is more or less the free algebras case (?).
Before altering the simp. T-complex page, I thought it worth asking this question of ’varieties’ as the answer (if it is known) would influence how best to do the edit.
Thomas's guest post at cafe and his paper should maybe be reflected in entry infinity-category and other places in nlab where various "models" fro infinity categories are listed, as it should have a very important role in my opinion, but still better experts should do carefully these changes. I might give a slightly uninformed interepretation of the role of this work in comparison to the experts like Mike.
brief category:people-entry for hyperlinking references at
started a minimum at M-wave
(I was after the kind of statement as cited by Chu-Isono there, but have added now a minimum of the background literature, too).
brief category:people-entry for hyperlinking references at equivariant differential topology
stub for Poincare lemma
some minimum, on occasion of today’s
brief category:people-entry for hyperlinking references at LHC and leptoquark
I am starting Deformation Theory
in the course of this I so far added links and an extra secton to Kähler differential and links to and from cotangent complex.
brief category:people-entry for hyperlinking references at cosmic censorship hypothesis and weak gravity conjecture
I decided that nLab is probably a better place to develop my ideas than ‘wikipedia’, where I posted one article on this topic but never felt confident to add more, since wikipedia is not really meant for ’ongoing research’. I really liked the idea of using this space for ’public notes on my research’ and am looking forward to getting reactions from some of you.
As a starter, I feel that using the first-person form in my reporting is more ’honest’ regarding the academic status of the piece. Prefix orders are not an accepted notion in literature yet, I think. The notion itself is used often, but always in a specific context and was (as far as I know) never generalized - until now…
Pieter Cuijpers
brief category:people-entry for hyperlinking references at
added hyperlinks to the text at induced representation. Made sure that it is cross-linked with Frobenius reciprocity.
brief category:people-entry for hyperlinking references at characteristic class of a linear representation
brief category:people-entry for hyperlinking references at characteristic class of a linear representation