(no subject)

[leblon]

Anybody knows how to define spin structure on a triangulated Riemann surface combinatorially? (The 3d analog would also be interesting). Should it be something like picking a 1-simplex in every 2-simplex in some consistent way?

Comments

[sasha-br.livejournal.com]

У тебя udod не в друзьях? Он наверняка знает.
Если нет, то я могу перепост сделать (меня он, вроде, читает).

[jedal]

AFAIR (for any cell structure) spin structures are in bijection with (equivalence classes of) Kasteleyn orientations (orientations of edges of the 1-skeleton, such that the product of relative orientations of boundary edges of each face is negative).

[pasha-m.livejournal.com]

I heard a general construction from David Cimasoni, you might ask him.

[leblon.livejournal.com]

Right. To be precise, "relative orientation" means "relative to an orientation of the surface".

[leblon.livejournal.com]

By "general" do you mean in all dimensions? I saw his papers with Reshetikhin about the 2d case, in connection with the dimer problem.

[pasha-m.livejournal.com]

Yes, I mean general dimension. I might be wrong though, we talked quite a while ago.