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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 6th 2011
   • (edited Feb 6th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexA 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 $n$-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 $$ Spin(X) \to Top(X,B SO) \stackrel{(w_2)_*}{\to} Top(X, B^2 \mathbb{Z}_2) \,. $$ I have added one reference that explicitly discusses the groupoid of spin structures to [[spin structure]]. Do you have further references?

   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 $n$-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

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

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

   Do you have further references?

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 7th 2011
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItex@Urs This looks worth pursuing. It may relate to HQFTs. We can discuss this when you arrive (in Lisbon).

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

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexHow 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.

   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.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeFeb 7th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownUrs, you skipped Lisboa ?

   Urs, you skipped Lisboa ?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Urs, you skipped Lisboa ? No, I'll go. My flight is day after tomorrow, Feb 9.

   Urs, you skipped Lisboa ?

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