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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 6th 2011
    • (edited Feb 6th 2011)

    A manifold has

    • a set of orientations;

    • an xyz of topological spin structures

    • a 3-groupoid of topological string structures;

    • a 7-groupoid of topological fivebrane stuctures, etc.

    and for some reason it is common in the literature (which of course is small in the last cases) to speak of these nn-groupoids, but not so common to speak of the xyz here:

    • A manifold has a groupoid of spin structures.

    Namely the homotopy fiber of the second Stiefel-Whitney class

    Spin(X)Top(X,BSO)(w 2) *Top(X,B 2 2). Spin(X) \to Top(X,B SO) \stackrel{(w_2)_*}{\to} Top(X, B^2 \mathbb{Z}_2) \,.

    I have added one reference that explicitly discusses the groupoid of spin structures to spin structure.

    Do you have further references?

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 7th 2011

    @Urs This looks worth pursuing. It may relate to HQFTs. We can discuss this when you arrive (in Lisbon).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2011

    How is it going in Lisbon? I hope it’s sunny. I need some sun. Though today it seems winter is taking a break even here.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeFeb 7th 2011

    Urs, you skipped Lisboa ?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2011

    Urs, you skipped Lisboa ?

    No, I’ll go. My flight is day after tomorrow, Feb 9.