under construction
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
In analogy to how the Lie group spinᶜ 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
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)
Haibao Duan, Fei Han, Ruizhi Huang, Structures and Modular Invariants, Trans. AMS 2020 (arXiv:1905.02093)
The push-forward in twisted tmf induced by a -structure is discussed in
A discussion explicitly in the context of string theory is in
Their smooth refinement and their smooth moduli 2-stacks were introduced in
see also
Last revised on July 5, 2024 at 13:49:20. See the history of this page for a list of all contributions to it.