Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology natural nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 6th 2010

    recorded two references to physics application at exotic smooth structure

    (no time for anything else)

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2010

    Torsten Asselmeyer-Maluga added a reference to an article of his

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeSep 6th 2010
    many more references added, did I miss something?
    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeSep 7th 2010
    • (edited Sep 7th 2010)

    Yes, lots of references added by Torsten, and thanks for them!

    Tip: Instead of creating Torsten Asselmeyer, add [[!redirects Torsten Asselmeyer]] to the bottom of Torsten Asselmeyer-Maluga. (I have fixed this now.)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 7th 2010

    many more references added

    There is this long list of references by Jerzy Krol (a whole subsection). Did anyone look at this?

    I think the majority of the references by him have nothing to do with exotic smooth structure – and don’t claim to have. It’s just the two joint papers with Torster Asselmeyer-Maluga that do.

    So I think that section with references of Krol should not be in this entry.

    In this long series of articles currently listed at exotic smooth structure Krol speculates aout possible applications of topos theory and other abstract category theory to physics. For instance he asks

    • whether at small scales spacetime might have to be modeled by a general topos instead of a topological space,

    • whether model theory might explain the AdS/CFT correspondence,

    • whether non-standard integers in the Basel topos of synthetic differential geometry might explain how to handle divergencies in quantum field theory.

    Things like that. I think these are in principle interesting questions (though I don’t understand what he means in the AdS/CFT case) but that they remain very speculative.

    I would suggest we move this list of publications by Krol to a different entry, say to n-categorical physics and add comments indicating that this is speculative.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 7th 2010

    Something mathematical at exotic smooth structure, namely an idea section and reference to Milnor’s 7-sphere paper.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 7th 2010

    Thanks. I edited it a bit, check if you like it.

    Maybe you find a second to add the references that you allude to to the References-section. That would serve to counterbalance the huge list of potential physical applications with a little bit of genuine substance :-)

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 7th 2010
    • (edited Sep 7th 2010)

    Oh, and I created a stub for topological manifold directing to manifold (where there is detailed discussion).

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 7th 2010

    I suggest

    I have now created a “category: people”-entry Jerzy Krol and for the moment moved his list of publications to there.

    • CommentRowNumber10.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 8th 2010

    A little bit more, but I’ll just leave links to Wikipedia pages for references (of which there are a number) at the moment

    • CommentRowNumber11.
    • CommentAuthorGuest
    • CommentTimeSep 10th 2010
    I know, the page should give only the idea but I add some technical things in a general style.

    The reference list for the applications to physics is nearly complete. I have no idea what else. I remember on a proceeding paper by Penrose quite after the appearance of Donaldson reults (in 1983). There, he speculates about exotic smoothness and its relation to physics vis the anti-self-dual solutions. I will look for that paper.

    There are two constructions for exotic compact 4-manifolds: the knot surgery and the Akbulut cork which should be discussed....
    Or is the article to long?

    Torsten
    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2010

    I know, the page should give only the idea

    No, this is not a demand we have on the page! It’s just that so far nobody had the energy to do more.

    I add some technical things in a general style.

    Good, thanks. If you feel like expanding this entry to a more comprehensive technical discussion, that would be great. Maybe have a look at our template page for inspiration.

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMar 24th 2021

    added DOI and pdf-link for:

    diff, v43, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)