nLab stringor bundle




In a higher version of how a spin structure induces spinor bundles, so string structure on a manifold transgresses into a kind of spin structure on its free loop space, which is “fusive” with respect to fusion of loops (along trinions). Equipped with this structure this should be a 2-vector bundle on the base space, and this is what is called the stringor bundle.


The idea that String structure on a manifold is a kind of spin structure on its loop space is due to

  • Edward Witten, The Index Of The Dirac Operator In Loop Space Proc. of Conf. on Elliptic Curves and Modular Forms in Algebraic Topology Princeton (1986) (spire)

The idea and the terminology of “stringor bundles” originates with:

An actual construction appears in:

Reviewed in:

Compare also

and other references at smooth loop space.

Last revised on February 15, 2024 at 16:44:27. See the history of this page for a list of all contributions to it.