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
Hisham Sati, Urs Schreiber, Jim Stasheff, Def. 23 on p. 47 with Prop. 21 on p. 48 in: $L_{\infty}$ algebra connections and applications to String- and Chern-Simons $n$-transport, in Quantum Field Theory, Birkhäuser (2009) 303-424 [arXiv:0801.3480, doi:10.1007/978-3-7643-8736-5_17]
Hisham Sati, Urs Schreiber, Jim Stasheff: middle boxes on p. 28 and p. 32 of: Twisted Differential String and Fivebrane Structures, Communications in Mathematical Physics 315 1 (2012) 169-213 [arXiv:0910.4001, doi:10.1007/s00220-012-1510-3))]
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:
Konrad Waldorf, Geometric T-duality: Buscher rules in general topology, arXiv:2207.11799.
Thomas Nikolaus, Konrad Waldorf, Higher geometry for non-geometric T-duals, arXiv:1804.00677.
Last revised on January 11, 2024 at 02:49:06. See the history of this page for a list of all contributions to it.