nLab adjusted connection


A notion of connection for principal ∞-bundles that does not impose the fake flatness condition.


The construction of non-fake flat principal ∞-connections originates with

based on the adjusted Weil algebras discussed earlier in

As the title of FSS 12 indicates, this procedure constructs Čech cohomology cocycles for non-fake flat higher connections in the style of the cocycles in

for the underlying bundles.

This construction is based on the Lie integration of L-infinity algebras by the “path method” and as such works generally but produces very “large” cocycle data, in a sense.

A variant construction tailored towards “smaller” cocycles for low-degree Lie n-algebras was later proposed in:

Examples for T-duality:

Further references for T-duality:

Last revised on January 11, 2024 at 02:49:06. See the history of this page for a list of all contributions to it.