Timeline for "Lie theory" for anchored bundles and reflexive graphs
Current License: CC BY-SA 4.0
3 events
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| Nov 14, 2020 at 0:29 | comment | added | Bertram Arnold | Integration of $L_\infty$-algebras is done by solving a Maurer-Cartan equation - compare arxiv.org/abs/2010.10485 . For $L_\infty$-algebroids, one has to include smooth simplices, as in the $A$-paths you mentioned. In the absence of a bracket, the only thing you can write down is this ODE; in general, you can define "L_\infty algebroids up to order $n$" by asking that the CE-differential squares to something in form degree $>n$, and make sense of the integration up to simplicial degree $n$. This should be a cofree construction, i.e. maps into it have a universal property. | |
| Nov 13, 2020 at 18:09 | comment | added | Ben MacAdam | Thanks, this looks great. I have two questions: 1. Is this construction basically going Anchored bundle with connection $\to$ free $L_\infty$-algebroid $\to$ free $\infty$-groupoid $\to$ the truncation? 2. Is there a reference you can point me to - I am familiar with the A-paths construction from Crainic and Fernandes's notes, but this seems a bit more general. | |
| Nov 13, 2020 at 8:48 | history | answered | Bertram Arnold | CC BY-SA 4.0 |