I've been watching Tachikawa's talk.
Recent advances in Supersymmetry
around 38 minutes he talks about objects in H3(M,ZN) with the property that
∫Ca∈ZN
He says due to self duality in 6D dimensions two intersecting cycles C and C' with C∩C′≠0 are mutually non local.
It seems that mutually non-local means ∫Ma∧b≠0
But why is this true, what happens when a theory is self dual?
What happens when you add supersymmetry?
He talks about the self dual 3 form what about other fields in the theory?
Is there a fermionic(or supersymmetric) generalization to H3(M,ZN)?
What is the recipe to construct the partition vector?
Is there any detailed exposition of the subject ? What books discuss the object H3(M,ZN)? I am familiar with the basic ideas of co-homology for U(1) gauge groups, but I have never really studied its generalization to other gauge groups.
Please excuse me if my questions are naive or too simple.
Edit: I have attached the related slides


