Not signed in (Sign In)

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-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor 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 limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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 sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft 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).
  1. Added Thom-Federer and Gottlieb thorems to Eilenberg-MacLane space; added the remark “ΩC(X,Y)C(X,ΩY)\Omega\mathbf{C}(X,Y)\simeq \mathbf{C}(X,\Omega Y) in any (oo,1)-category with homotopy pullbacks” in loop space object.

  2. created stub for Hodge star operator

  3. added a few remarks on Eilenberg-Mac Lane space and Whitehead tower.

    • CommentRowNumber4.
    • CommentAuthordomenico_fiorenza
    • CommentTimeJul 22nd 2010
    • (edited Jul 22nd 2010)

    at String Lie 2-algebra I guess CE(𝔰𝔱𝔯𝔦𝔫𝔤(n))=( 𝔤 *b,d 𝔰𝔱𝔯𝔦𝔫𝔤)CE(\mathfrak{string}(n))=(\wedge^\bullet\mathfrak{g}^*\oplus\langle b\rangle,d_\mathfrak{string}) should rather be

    CE(𝔰𝔱𝔯𝔦𝔫𝔤(n))=( (𝔤 *b),d 𝔰𝔱𝔯𝔦𝔫𝔤)CE(\mathfrak{string}(n))=(\wedge^\bullet(\mathfrak{g}^*\oplus\langle b\rangle),d_\mathfrak{string}).

    waiting for feedback on this before editing the page.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2010


  4. ok, I’ll now edit that and add the explicit expression for the 3-brackets.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2010

    Thanks for taking care of that!

  5. done. when you have time, please check.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2010
    • (edited Jul 22nd 2010)


    I added a section on how 𝔰𝔱𝔯𝔦𝔫𝔤\mathfrak{string} is the b𝔲(1)\mathbf{b}\mathfrak{u}(1)-principal \infty-bundle over 𝔰𝔬\mathfrak{so} classified by the cocycle μ:𝔰𝔬b 2𝔲(1)\mu : \mathfrak{so} \to \mathbf{b}^2 \mathfrak{u}(1) .

  6. Leaving for two weeks: holiday :)

    Have a nice time,


  7. added a line just after equation (1) in group extension.

  8. Expanded coset.