Special and general types
Higher spin geometry
Critical string models
In analogy to how the Lie group spin^c is obtained by twisting the lift through the second stage of the Whitehead tower of by the first Chern class
there is a similar twist by the second Chern class of the lift through the next stage of the Whitehead tower
Accordingly a lift of the structure group to is a -structure.
For the moment see at twisted smooth cohomology in string theory for more.
Topological -structures were introduced
- Bai-Ling Wang, Geometric cycles, index theory and twisted K-homology. J. Noncommut. Geom., 2(4):497–552, 2008.
and shown to induce a twisted Witten genus in
Qingtao Chen, Fei Han, Weiping Zhang, Generalized Witten Genus and Vanishing Theorems, Journal of Differential Geometry 88.1 (2011): 1-39. (arXiv:1003.2325)
Jianqing Yu, Bo Liu, On the Witten Rigidity Theorem for Manifolds, Pacific Journal of Mathematics 266.2 (2013): 477-508. (arXiv:1206.5955)
The push-forward in twisted tmf induced by a -structure is discussed in section 11 of
- Matthew Ando, Andrew Blumberg, David Gepner, Twists of K-theory and TMF, in Robert S. Doran, Greg Friedman, Jonathan Rosenberg, Superstrings, Geometry, Topology, and -algebras, Proceedings of Symposia in Pure Mathematics vol 81, American Mathematical Society (arXiv:1002.3004)
A discussion explicitly in the context of string theory is in
Their smooth refinement and their smooth moduli 2-stacks were introduced in
A general discussion is in section 5.2 of
Revised on March 22, 2014 05:26:29
by Urs Schreiber