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Aug 17, 2017 at 22:57 comment added cheyne I know this is a bit late, but I'm pretty sure your answer is here: arxiv.org/pdf/0907.2566.pdf
Feb 17, 2016 at 17:39 comment added cheyne I wish I could say this was an "answer", but my educated guess is that you allow for 1,2, and 3-holonomy to all live in different structure groups. That means you need a 3-form a 2-form and a 1-form on an open set to give a connection. Now you need to transform 3-holonomy along an intersection so you'd need a 2-form (acting on the "faces" of the 3-track) in addition to the other information from the 2-connection story. In short: A triplet $C_i, B_i, A_i$ and a triplet $c_{ij}, a_{ij}, g_{ij}$.
Apr 27, 2014 at 15:57 history edited geodude CC BY-SA 3.0
added 87 characters in body; edited title
Apr 27, 2014 at 15:24 history asked geodude CC BY-SA 3.0