Timeline for Is there a higher homotopical spinor theory?
Current License: CC BY-SA 2.5
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| Nov 29, 2010 at 22:37 | comment | added | Urs Schreiber | ... the Whitehead tower of the orthogonal group fivebrane -> string -> spin -> so -> o . There is a refinement in differential cohomology of the obstructions classes to these higher lifts, and these yield the famous "anomaly poloynomials" in heterotic string theory and in electric-magnetic dual heterotic (= fivebrane) theory. | |
| Nov 29, 2010 at 22:34 | comment | added | Urs Schreiber | By the way, if "higher spinor" is interpreted in the sense of quantum field theory, then it is not (at least not directly) the Stiefel-Whitney classes that correspond to higher spin structures, but the higher fractional Pontryagin classes: a 1-dimensional supersymmetric sigma model QFT exists on a target space that has spin structure, a 2d susy QFT on a target that has in addition a string-structure, obstructed by p1/2, then a 6d SQFT on a target that has what was called a fivebrane structure, obstructed by p2/6. And in fact a 0d susy QFT needs an orientation. So we are lifting here through... | |
| Nov 29, 2010 at 18:33 | comment | added | Jacob Lurie | Should be easy enough to make it central: form the fiber product in simplicial groups, where you can model K(Z/2, m+1) and its path space by simplicial abelian groups. More generally, I believe that simplicial objects in "groups with a central extension" is a model for the homotopy theory of triples (X,Y,f) where f is a pointed connected space, Y is a 1-connected HZ-module spectrum, and f is a map from X to the zeroth space of Y. | |
| Nov 29, 2010 at 17:01 | comment | added | Angelo | Thanks, I'll think about it (simplicial homotopy theory is really not my field, I need time to digest about it). I meant to ask for a central extension, though. | |
| Nov 29, 2010 at 16:00 | history | answered | Charles Rezk | CC BY-SA 2.5 |